Thinly slice the onions, chop the garlic and cut the peppers into thin strips, removing the seeds and white membranes. Score a cross in the tomatoes, plunge them into boiling water for 30 seconds, then peel and roughly chop them.

In a large frying pan or sauté pan, heat the olive oil and gently fry the onions over a low heat for 5 minutes. Add the garlic and cook for 1 minute.

Add the peppers and let them soften over a medium heat for 10 minutes, stirring from time to time.

Add the tomatoes, thyme, bay leaf, sugar, salt and Espelette pepper. Simmer uncovered for 30 minutes, until the cooking juices have almost completely evaporated.

If you are serving Bayonne ham, quickly sear the slices in a hot frying pan, 30 seconds on each side.

For the version with eggs, make four small hollows in the piperade, crack the eggs into them, cover and cook for 5 minutes. Serve with the ham and a pinch of Espelette pepper.