1. Cook the noodles according to package directions. Reserve 1/2 cup of the cooking liquid, drain the pasta and return it to the pot.
2. Meanwhile, heat a large skillet over medium heat. Add the pancetta and cook, stirring occasionally, until crisp, 5 to 7 minutes. Using a slotted spoon, transfer to a paper towel-lined plate. Pour off and discard about half the fat (you should have about 1/4 cup left in the pan).
3. Add the peppers to the pan and cook over medium heat, stirring occasionally, until tender, 5 to 7 minutes. In a large bowl, toss the pasta, cheese and 1/4 cup of the reserved pasta water (adding more water if the pasta seems dry. Fold in the peppers and pancetta, then the basil.