Bring a large pot with lightly-salted water to a boil. Stir the penne into the water and return to a boil. Cook until the pasta is mostly tender but still firm to the bite, about 11 minutes; drain. Transfer the drained pasta to a large bowl.
Place the basil, red pepper, and Parmesan cheese in the bowl of a food processor; stream the olive oil into the mixture as it blends until smooth. Season with salt and pepper. Drizzle the sauce over the cooked pasta and toss to coat.