Sauté green pepper very slowly in pork fat or olive oil. Add onion and tomatoes with garlic and ham. Season to taste with salt and freshly ground black pepper, and simmer mixture slowly until the vegetables are rather soft.
Beat 4 eggs lightly, season to taste and stir gently into hot vegetable mixture. Be sure not to let them overcook, for this Basque omelette should be soft and wet, almost the consistency of scrambled eggs. Serve on a hot platter.