Meanwhile, pluck the basil leaves from the stems (you should have about 2 cups leaves). Wash the leaves in a large bowl of cold water and dry in a salad spinner or pat dry with paper towels. Smash and peel the garlic.
Put the basil, garlic, and pine nuts in a food processor and pulse until coarsely chopped. With the processor running, gradually add the olive oil and process until the pesto is smooth. Transfer the pesto to a large bowl and stir in the cheese. Season with the salt and some pepper.
Bring a large pot of cold water to a boil over high heat and salt it generously. Add the penne and boil, stirring occasionally, until al dente, about 8 to 10 minutes. Drain in a colander and save about 1/4 cup pasta cooking water. Add the pasta to the bowl. Use tongs and toss with enough of the cooking water so the pesto coats the pasta evenly. Season with salt and pepper. Serve warm.
Upgrades: a. Make the pesto creamy by adding 1/4 cup ricotta cheese when processing the basil, garlic, and pine nuts. This is great with tortellini or ravioli. b. Top dressed pesto pasta with 1/2 pound diced large or halved small fresh mozzarella balls (bocconcini), 3 medium tomatoes cut in large chunks, and 1/2 cup pitted black olives, (we like kalamata for this), roughly chopped. c. Add cooked 1 to 2 cups chicken or shrimp.
Twists on Pesto: In place of basil, try the following combination: 1 cup parsley, 1 cup fresh spinach leaves, 2 tablespoons fresh rosemary leaves, 2 tablespoons fresh thyme leaves. Substitute walnuts for the pine nuts
Pesto freezes beautifully. If you know your batch is headed to the deep chill, don't add the cheese. Adding the cheese right before serving brightens the flavor and avoids a gummy texture.