In a large saucepan, warm 2 tablespoons duck fat over medium heat. Add the jambon and garlic, and cook, stirring, until lightly browned, about 6 minutes. Add the padrón peppers and onions to the pan and cook, stirring, until softened and lightly browned, about 14 minutes. Stir in the tomato paste, cook for 2 minutes, then add the piquillo peppers along with the tomatoes, parsley, thyme, and bay leaf. Season the peppers with salt and piment d'Espelette and cook, stirring occasionally, until the tomatoes break down and the pipérade is thickened but still loose, about 10 minutes. Scrape the pipérade onto a serving platter and keep warm.