Aromatic smoke wafting from a grill on a Lima street can only mean one thing: anticuchos, the city’s favourite night-time snack of sliced meat – traditionally beef heart, marinated in ají panca (a hot, smoky chilli), cumin, black pepper, garlic and vinegar – skewered and grilled.

The Inca take on kebabs was made with llama, but in the 1500s the Spanish brought African slaves and new ingredients, including cattle and spices. And it was the slaves who created today’s anticuchos, taking inspiration from heavily seasoned Andean meat as they thought up ways to cook the offal the Spaniards wouldn’t eat.

Fast-forward to the 1970s and Grimanesa Vargas was serving the city’s finest anticuchos from a humble grill-on-wheels in Miraflores. As her fame grew, so did the queues for her melt-in-the-mouth skewers – even Gastón Acurio, celebrity chef and champion of Peruvian cuisine, was a fan.

Vargas says there’s no secret recipe – just hard work and good meat cooked with love. Now also a celebrity, she opened a namesake restaurant in 2011 not far from her street corner.

Since Peru became a foodie hotspot, street food has transcended social class. Acurio serves up posh anticuchos at Panchita and, last year, young chef Brandon Altamirano – who won best anticuchero in Acurio’s TV reality show Anticucho Con Corazón (“anticucho with heart”) – opened Anticuchos Bran in Surquillo, where you can mix up pork, chicken and beef heart.

And you can still find anticuchos on the street, served with boiled potatoes and choclo (giant corn). The grills are out in force in late October around the historic Las Nazarenas church, when the venerated image of the Señor de los Milagros (Lord of Miracles) – painted by an African slave in the mid-17th century – is taken on a days-long procession.

Running until 5 November, the 10th anniversary of Lima’s gastronomy fair Mistura – the largest in Latin America – celebrates Peru’s culinary traditions with top chefs, a farmers’ market and classic dishes, including Grimanesa Vargas’s anticuchos.