How to Make It
In a large skillet, heat the olive oil. In a small bowl, toss the capers with the cornstarch and transfer to a sieve; shake off the excess cornstarch. Add the coated capers to the oil and fry over high heat, tilting and gently shaking the pan, until the capers are crispy and golden, about 3 minutes. Drain the capers, reserving 2 tablespoons of the oil in the skillet. Spread the capers on a paper towellined plate.
Add the anchovies and garlic to the skillet and cook over high heat, stirring, until the garlic is golden and the anchovies dissolve, about 3 minutes. Add the prosciutto, separating the ribbons, and cook until lightly browned, about 1 minute. Add the tomatoes and crushed red pepper and cook just until the tomatoes begin to break down, about 3 minutes. Stir in the basil.
Meanwhile, in a large pot of boiling salted water, cook the pasta until al dente. Drain, reserving 1/2 cup of the cooking water. Return the pasta to the pot along with the water and pour the sauce on top. Toss over high heat just until the sauce is thickened, about 2 minutes. Serve the pasta in bowls, garnished with the crispy capers. Pass the grated cheese at the table.