Bring a large pot of salted water to boil for the pasta. Wash the tomatoes, remove the stems, and cut into halves or quarters, depending on their size. Cut the prosciutto into bite sized strips (remembering that they will shrink when cooked.) Slice the onions very thinly.
In a large skillet over medium heat, add the onions to the olive oil and sauté until lightly golden. Add the prosciutto and sauté for an additional minute or two, or until it begins to darken, but not allowing it to become crispy. Add the tomatoes, and salt and pepper to taste. Cook for about 10-15 minutes, until the tomatoes soften and release their juice. Meanwhile, cook the pasta until 1 minute less than al dente and drain it. Add the pasta to the tomato sauce and cook together over medium heat for an additional minute. Serve immediately, sprinkled with Pecorino cheese.