Having spent every childhood holiday and whole summers of my 20s in France, I fancied I knew the place a little. I’d skidded down its mountains in winter, and done my time in the August jams on the autoroute du soleil – but when I set off to cycle around the country for a book a couple of years ago, I realised that I’d barely scratched the surface, especially when it came to food.

Of course, I was happily familiar with the big hitters like coq au vin and moules marinère, that represent French cuisine abroad, and I had more than a passing acquaintance with the powerful southern flavours of Provence. But much French regional cooking is far subtler – despite the popular stereotype, it wasn’t until I hit Marseille that I really tasted garlic.

As I tucked into my umpteenth plate of perfectly poached white fish in beurre blanc sauce, I couldn’t help but think wistfully of the fiery mustards and hot sauces sitting on my shelf at home. Not that these things aren’t eaten and enjoyed in France, of course, but if you stick to classic French restaurants, you’re unlikely to come across them very often.

Then, a few weeks in, I had a revelation. It came after a very wet 83 miles in the saddle in the misty shadow of the Pyrenees, in the city of Pau, home of poule au pot. This simple chicken and vegetable stew occupies a sacred place in the French heart, largely thanks to its associations with Good King Henry, king of France from 1589-1610. But 400 years later, sitting in the cosy dining room of the redoubtable Chez Olive, looking at the steaming pile of beige in front of me, its attractions were not immediately obvious. Sitting in a puddle of murky broth were pale chicken, ghostly turnips and a pallid cabbage leaf stuffed with something brown. The Chez Olive was a fixture of the local food scene for over 70 years until it sadly closed earlier this year.

Yet from the first mouthful of the delicately savoury liquor, with its golden coins of floating fat, it was clear this dish needed nothing more. No splodge of lime pickle or dash of malt vinegar could have improved this perfectly balanced, wonderfully soothing dish. It was a bowl of pure bliss. And, as I slurped and the rain still poured, I reflected that I’d been missing the point. Old-fashioned French cooking is polite: it strives for the harmony of quietly complementary flavours rather than the discordance of big, loud, clashing ones. There are, I’m sure, wider parallels to be drawn here … but I just do food.

Poule au pot à la facon de Chez Olive

The stuffing and vegetables are there to stretch the weekly chicken further, but in fact make it a complete dish in its own right. At Chez Olive they serve it with rice, which is also a nice way to soak up the copious broth. This is a dish that it’s well worth buying a good chicken for – by which I mean a chicken that’s lived life a bit, and had a chance to develop some flavour. They’re much harder to find in the UK than France: if you can’t get to a butchers or farm shop, try online. (I found one with feet, which was thrilling, but not strictly necessary.) The bird doesn’t need to be huge, as there’s enough other stuff here to keep everyone happy.

Serves 4-6

For the stuffing
A knob of butter
2 banana or 4 round shallots, finely chopped
2 plump garlic cloves, finely chopped
2 sprigs of thyme, leaves picked
A good grating of nutmeg
4 chicken livers
420g sausage meat (about 6 sausages’ worth)
75g fresh white breadcrumbs
2 tbsp armagnac or other brandy

1 good chicken, about 1.8kg
6 large savoy cabbage leaves
2 litres chicken stock
1 tsp peppercorns
4 small leeks, trimmed or 2 large ones, cut into thick chunks
4 small carrots scrubbed, or 2 large ones, cut into thick chunks
12-16 small new potatoes
4 small turnips, cut in half if on the larger side or 1 large one cut into chunks

For the sauce blanche
1 tbsp butter
1 tbsp flour
2 tbsp creme fraiche

Start with the stuffing. Melt the butter in a small frying pan over a medium-low heat and sauté the shallots until soft, then add the garlic, thyme leaves and nutmeg. Fry for a couple more minutes, then allow to cool.

Meanwhile, finely chop the livers, discarding any stringy bits, and put them in a large bowl. Add the sausage meat and breadcrumbs and stir in, then add the brandy and season. Mix well.

Put roughly ⅔ of the stuffing inside the chicken, then either sew the neck up, or use cocktail sticks to secure it (my preferred method).

Bring 1.75 litres of chicken stock to the boil in a large pot with the peppercorns, and add the chicken. Bring back to the boil, then turn down the heat and simmer very gently for 45 minutes, then add the vegetables and cook for 30-45 minutes more until both the chicken and the vegetables are done (if the chicken’s juices run clear from the thickest part of the thigh before the veg is done, lift it carefully out of the pot and set aside to keep warm, then turn the heat up under the pan).

Meanwhile, bring a pan of salted water to the boil. Carefully cut out the base of the tough central core from the cabbage leaves and discard, then blanch them for 2 minutes and cool under cold running water to stop them cooking any further. Dry well.

Stuff the cabbage leaves by rolling a generous tablespoon of the remaining stuffing mixture into a short cylinder at the base of one of the leaves, above the cut stem, then tuck in both sides and continue rolling to the top of the leaf. Repeat with the rest of the cabbage leaves, then place, seam-down, in the base of the large saucepan. Tip in the remaining 250ml stock and bring to a simmer. Cover with a lid and turn the heat down very low. Cook for 45 minutes then turn off the heat but leave covered to keep warm.

Once the chicken is done, keep it warm while you make the white sauce, if serving. Melt the butter in a small sauce pan and then stir in the flour and cook for a couple of minutes. Gradually, spoonful by spoonful, whisk in the chicken stock the cabbage rolls were cooked in. Once it’s smooth, take off the heat and stir in the creme fraiche. Season to taste.

Carve the chicken and divide between shallow bowls with the stuffing, the cabbage rolls, vegetables and a good ladleful of broth. (If the middle of the stuffing looks pink, and this worries you, fry it briefly in a hot pan.) Serve with the white sauce, and steamed rice if you’d like to bulk it out further.

• From One More Croissant for the Road by Felicity Cloake (Mudlark, £9.99). To order a copy for £9.29, go to guardianbookshop.com