Place the roasted peppers and chiles and sauce (if using) in the bowl of a food processor fitted with the steel blade. Add the minced fresh garlic, cooked garlic (if using), and the pine nuts and pulse to chop everything small. Add 1 cup of the oil and a generous amount of black pepper and process until the pesto is almost pureed but still retains some texture. If not planning to freeze, add the cheese and some salt to taste. Process just to combine.

Remove as much pesto as needed and, before storing the rest in the refrigerator, pour a generous layer of olive oil over the top. Keep refrigerated in a well-sealed sturdy container. Bring the pesto to room temperature before each use. See Basil Pesto for do-ahead instructions.