Bring a large pot of salted water to a boil. When the water is thoroughly boiling, add the pasta and cook according to the package directions until al dente.
In a large skillet or shallow Dutch oven over medium-low heat, heat 1 tablespoon olive oil and cook the pancetta to render the fat and crisp it, about 8 minutes. Remove to a paper towel-lined plate to drain. Pour off and discard all but 1 tablespoon fat from the skillet. Raise the heat to medium and add 1 tablespoon olive oil. When the oil is hot, add the shrimp, garlic and red pepper flakes. Stir quickly and often so the garlic does not burn, 2 minutes at the most; the shrimp should be slightly undercooked.
Remove the shrimp to a warm bowl. Move the skillet off the heat. Drain the pasta, reserving about 1/2 cup pasta water. Add the hot pasta to the skillet or Dutch oven and return to medium heat. Add the pancetta, shrimp and reserved pasta water. Drizzle with the remaining 2 tablespoons olive oil. Toss and stir until the juices are combined and the shrimp is cooked through, about 3 minutes. Remove from the heat and add the chile peppers, cheese and basil. Do not stir. Serve immediately, family-style.