Prepare the piperade by first heating the 4 tablespoons of fat of your choice in a heavy 8-inch frying pan or, better still, in a small oval copper or enamel pan that you can bring to the table. Add the chopped onions and garlic and cook them for about 5 minutes over moderate heat, stirring them frequently until they are soft but not brown. Stir in the pepper strips, turning them in the fat now and then, letting them cook for about 10 minutes, at which point they should be tender but still crisp. Drain the chopped tomatoes thoroughly and add them to the pan, sprinkling in at the same time the dried or fresh basil and the pepper flakes or hot pepper sauce. Raise the heat and cook the tomatoes briskly for a few minutes and stir constantly with a wooden spoon until all their moisture has evaporated. Be careful that the piperade doesn't burn. Put it aside until you are ready to reheat and serve it.
At that point, combine 1 tablespoon each of olive oil and butter in an 8-inch heavy frying pan, and over moderate heat, cook the julienned ham for a few minutes until the strips are thoroughly heated through. Remove them at once with a slotted spoon and spread them out on paper toweling to drain.
Meanwhile let the fat in the frying pan cool to lukewarm before pouring it into the eggs, lightly beaten with salt and pepper. Over low heat, stir the eggs with a rubber spatula until they begin to form soft, creamy curds. Remove them from the heat when they are not quite set and gently spread them over the reheated piperade. Let some of the colorful vegetables show through. Lightly scatter the ham on top, sprinkle with the chopped parsley and/or chopped chives, and serve at once.
Recipe courtesy of Michael Fields, Culinary Classics and Improvisations, Random House, 1967