It was autumn in Venice. Pale mist hung over the canals in the early mornings before vaporising as the sun rose, and the city dressed up in its familiar, magical brocade of opulence and decay, like a raddled courtesan donning her finery for one last flourish. It should have been a time of melancholy, as my great adventure – spending six months pottering around the Italian islands on a Vespa – came quietly to an end in this, the most romantic and melancholy of all cities.

But it wasn’t remotely melancholic. I’d met my daughter, Lois, and my old Australian chum and former rugby compadre, Rory, beneath the lions in the Piazza San Marco, and gloom and despondency proved impossible in their humorous and diverting company. The day we met, we’d dashed off to a Venetian version of a crowded English pub to watch Australia trounce England in the Rugby World Cup, a victory that naturally had to be celebrated with numerous beers and several bottles of prosecco. That rather set the pace and the tone for the days that followed – high spirits, the rambling anecdotes of two old codgers, the amused tolerance of my daughter, food here and there, drink there and here, and a dash of culture in between.

And then came lunch on Torcello, one of the many islands of the Venetian lagoon, where Ernest Hemingway spent several months writing his worst novel, the unreadably bad Across the River and into the Trees. These days Torcello is more famous for its cathedral Basilica di Santa Maria Assunta, an elegant Venetian/Byzantine hybrid with startling mosaics; and for the Locanda Cipriani, one of the great restaurants of the world.

The Locanda was created in 1934 by Giuseppe Cipriani, and blessed in subsequent years by the custom of Hemingway, Winston Churchill, our own dear Queen, Arturo Toscanini, Maria Callas, Nancy Mitford, Marc Chagall and other luminaries.

If I’m honest, it’s comfortably old-fashioned and terracotta-ish, but who wants to eat inside at the Locanda Cipriani on a brilliant autumn day? We settled outside under a shading pergola in the garden behind, warm with golden sunlight, lambent with colour, unexpectedly bosky, with barricades of roses, trimmed box hedges, velvet lawn and blossoming borders that wouldn’t be out of place in Surrey.

Great meals aren’t made by great food alone, although that helps; they’re made by time and place and people and company and occasion. The day was exquisite. The company was pure delight. The tablecloth was stiff with starch and glittered like snow. The sun gleamed on the glasses and cutlery. The service moved with the stately choreography, urbane charm and assured professionalism of long practice. From the moment our waiter gently directed me away from the pinot grigio I’d suggested to a cheaper and immeasurably better pinot bianco, I knew things were going to be all right, and so they were.

The dishes – tagliolini with bechamel sauce and smoked prosciutto; gnocchi with scampi and chanterelles; fish soup, john dory with tomatoes and capers; turbot with fungi porcini; roasted monkfish; pancakes filled with sweet ricotta and burnished in the flames of Cointreau; apple custard tart – came and went, genial and generous. Bottles of pinot bianco came and went. Grappas and coffees came and went. The afternoon came and went, all in one seamless, happy, laughter-strewn continuum. Lunch had the air of sublimity about it, of being outside time, of languid perfection.

Tagliolini verdi gratinati con prosciutto cotto affumicato e besciamella

Green tagliolini gratin with smoked ham and béchamel sauce

This is my recreation of the great original recipe. Any difference in quality between the original Locanda Cipriani dish and mine is entirely my responsibility.

Serves 4

250g green tagliolini
50g smoked ham cut into julienne strips
30g grated parmesan, plus extra
4g plain flour
50g butter
50ml milk
50ml white wine
1 bay leaf
nutmeg

For the béchamel sauce
Put the milk and wine in a saucepan with the bay leaf and a good grate of nutmeg. Bring to the boil, turn off and leave to steep and cool.

Melt 25g butter in a pan over a low heat. Add the flour and cook gently, stirring constantly for 4-5 minutes. Take the pan off the heat and vigorously whisk in the milk/wine until well blended. Return to the heat and cook over a medium heat, stirring constantly until it is creamy and smooth. Use a wooden spoon and be sure to stir the sauce from the bottom and the sides of the pot.

Add half the grated parmesan and cook gently for another 5 minutes, stirring frequently. Season with salt and pepper. Keep warm.

For the tagliolini
Bring a large pot of water to the boil, then add a tablespoon of salt.

If using fresh pasta cook in rapidly boiling water for two minutes; if using dried pasta it will take longer (I suggest one minute less than suggested on the packet). Either way it should be al dente. Drain it well.

Slice the ham into strips. Melt 1 tablespoon of butter in a sauté or frying pan over a medium heat. Add the ham, cooking for a minute or two, stirring. Add the tagliolini to the ham, adding a little butter. Toss well.

Spread the pasta evenly in a well-buttered casserole dish. Pour the béchamel sauce evenly over the top. Sprinkle any remaining cheese (and maybe a few strips of smoked ham) over the top. Cut any remaining butter into bits and scatter over the top. Brown (as lightly as possible) under a grill for one to two minutes.

• Matthew Fort is a food writer and critic who appears as a judge on The Great British Menu. He is the author of Eating Up Italy: Voyages on a Vespa (HarperCollins)