Bring a large pot of salted water to a boil and cook the pasta according to package instructions until al dente. Reserve 1/2 cup of the pasta cooking water before draining.
In a blender or food processor, combine the peas, fresh basil leaves, grated Parmesan cheese, toasted pine nuts or almonds, minced garlic, olive oil, lemon juice, salt, and pepper.
Blend the ingredients until smooth, adjusting the consistency with a tablespoon or two of the reserved pasta cooking water, if needed.
Toss the cooked and drained pasta with the pesto sauce until evenly coated.
Serve the Pea and Mint Pesto Pasta warm, garnished with additional fresh basil and a sprinkle of grated Parmesan cheese, if desired.