How to Make It
Roast the red peppers over a gas flame or under the broiler, turning occasionally, until charred all over. Transfer the peppers to a bowl, cover with plastic wrap and let cool. Peel, core and chop the peppers.
In a small skillet, toast the pine nuts over moderate heat until golden, about 4 minutes. Let cool.
Transfer the peppers and pine nuts to a blender. Add the garlic and whole basil leaves and blend until coarsely chopped. Add the olive oil and puree to a chunky pesto. Season with salt and pepper.
In a large saucepan of boiling salted water, add the pasta and cook until al dente. Drain and cool slightly under running water. Transfer the pasta to a bowl and toss with the pesto. Season the pasta with salt and pepper. Top with the chopped basil and pecorino and serve at room temperature.