Cook the pasta according to package instructions in a large pot of salted boiling water until al dente. Drain and set aside, reserving 1/2 cup of the pasta water.
In a food processor, combine the basil, spinach, Greek yogurt, olive oil, lemon juice, garlic, and Parmesan cheese. Blend until smooth and creamy. If the sauce is too thick, add a little reserved pasta water to reach your desired consistency.
In a large bowl, combine the cooked pasta and the green goddess sauce. Toss well to coat the pasta evenly.
Season with salt and pepper to taste. If desired, add more lemon juice for extra brightness.
Serve the pasta warm, garnished with cherry tomatoes and toasted pine nuts.