If you can find fresh peas, feel free to use them instead of the frozen peas. Slideshow: More Pasta Recipes
In a food processor with the motor running, drop in the garlic and finely chop. Add the nuts, cheese, 1 teaspoon salt and 1/2 teaspoon pepper and pulse to finely chop. Add the basil and pulse to finely chop. With the motor running, add the oil, blending to combine.
In a large pot of boiling salted water, cook the pasta until al dente. 4 minutes before the pasta is done, stir in the corn and peas. Reserve 3/4 cup of the pasta cooking water, then drain the pasta, corn and peas. Toss the pasta with the pesto and about half the reserved cooking water. Add more water for a looser consistency. Season with salt and pepper to taste and toss with basil leaves before serving.