Cook the peas according to the package instructions and drain. Cook the pasta until al dente according to the package instructions.
Meanwhile, add the basil leaves, mint leaves, pine nuts, garlic, 1/2 cup of the peas, 1/2 cup of the Parmesan and some salt and pepper to a food processor or blender. Turn on the machine, then drizzle in the olive oil while it mixes. Continue blending until combined, adding additional olive oil if needed. Set aside.
Heat the cream and butter in a small saucepan over medium-low heat. Stir in the remaining 1/4 cup Parmesan.
Drain the pasta and place in a serving bowl. Pour the cream mixture over the top, followed by the pesto. Add the remaining 1 cup peas, toss and serve immediately.