Add the peas to a blender. (Reserve 2 tablespoons if using frozen for garnish.) Then add the cheese, basil, garlic, salt, and pepper. Pour in ⅓ cup of the olive oil. Puree on high until smooth. Add the remaining olive oil and puree again.

Pour into a medium saucepan and heat over medium for about 5 minutes, stirring constantly, until warmed through.

Divide the pasta among four serving plates. Top each with an equal amount of pea pesto sauce. Garnish with whole peas, Parmesan, and basil leaves before serving.