Put a large pot of water on the stove over high heat for pasta. When water comes to a boil, add salt to water and cook pasta to al dente, with a bite to it.
In a large, deep skillet, preheated over moderate heat, cook garlic, onion, and crushed pepper in extra-virgin olive oil for 3 to 4 minutes. Add tomatoes and sauce or puree to the pan. When tomatoes come to a bubble, reduce heat to simmer. Season sauce with salt and pepper.
When pasta is cooked to al dente, drain well and set near stove. Sprinkle ribbons of sliced prosciutto and the green peas into the sauce. Stir to combine and heat peas through. Toss pasta with sauce and shredded basil. Keep turning pasta in sauce until basil wilts and pasta begins to absorb sauce, about 1 minute. Transfer pasta to a serving platter and garnish with a few whole basil leaves.
Serve with salad and grated cheese, for passing.