Bring a pot of water to a boil for the pasta.
Roast the peppers over a flame on the stovetop or under the broiler to blacken the skins all over. Place the peppers in a bowl and cover with plastic wrap until cool. Peel the skins and seed the peppers.
Place the roasted red peppers and chili peppers in a food processor and add the nuts, basil, oregano, garlic, salt and pepper. Add the cheese, turn the processor on and stream in the EVOO to form a thick sauce.
Salt the pasta water and cook the spaghetti to al dente. Reserve about 1 cup of the starchy cooking water; drain the pasta and return to the pot. Toss the pasta with the pesto and half of the starchy cooking water. Toss the pasta with the sauce for a minute or two to combine thoroughly, adding a little more starchy cooking water if necessary. Serve with more cheese and some torn basil leaves or finely chopped mint and parsley, if desired.