In the pressure cooker, put 2 tablespoons of olive oil. When it is hot put in the chicken, salt and pepper. Cook for 2 minutes then flip each piece of chicken and add salt and pepper. Add Bayonne/prosciutto ham and 1 or 2 pinches of Espelette pepper/cayenne or hot paprika. Stir and remove the chicken and ham.
Add 1 tablespoon of olive oil into the pressure cooker and the onions. Let them cook for 2 minutes at medium heat, stirring from time to time. Add the pepper and garlic. Stir and let them cook for 2 minutes in stirring 1 or 2 times. Add the tomatoes, thyme, a pinch of salt, and a pinch of sugar. Stir. Put the chicken on the vegetables. Add the white wine and let it reduce until there is no more liquid (keep an eye on it so it doesn't burn!). At last add the warm chicken stock.
Close the pressure. When the steam escapes, turn down the heat and cook according to the specified time (18 minutes for me).
Remove the thyme from the pressure cooker and serve on top of steamed rice. My family enjoys this with couscous.