Cook the fusilli and bow ties separately in a large pot of boiling salted water for 10 to 12 minutes until each pasta is al dente. Drain and toss into a bowl with the olive oil. Cool to room temperature.
In the bowl of a food processor fitted with a steel blade, puree the pesto, spinach, and lemon juice. Add the mayonnaise and puree. Add the pesto mixture to the cooled pasta and then add the Parmesan, peas, pignoli, salt, and pepper. Mix well, season to taste, and serve at room temperature.