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Trim fat from ham if necessary and cut slices in half lengthwise. Cut the halves into 1.5 cm wide (approximately 1/2 inch) strips. Rinse the chile peppers, cut lengthwise, remove the seeds, remove the ribs and finely chop.
Cook the pasta in boiling salted water until al dente and drain, reserving some of the pasta cooking water. Meanwhile, melt the butter in a skillet and sauté the chopped chile peppers. Add the oregano. Add the cooked pasta and ham to the skillet. Add 2–3 tablespoons pasta cooking water and season with coarsely ground pepper. Divide pasta between four serving plates, generously sprinkle with Parmesan cheese and serve immediately. Serve with a fresh green salad, if desired.