Dice tomatoes and set aside. Cook mushrooms in a bit of olive oil for a few minutes, until mushrooms release their liquid. Remove from heat and set aside. 

Combine the basil, garlic, pine nuts, and 1/2 cup of the oil in a blender and pulse until somewhat coarse. Season with salt and pepper. Add the remaining oil and blend at medium speed until smooth. Transfer the pesto to a serving bowl and mix in the cheese.

Cook the cavatappi according to package directions. Drain and return to pot. Stir in the basil pesto until noodles are well covered. Toss in tomatoes and mushrooms and serve immediately. Garnish with basil leaves and grated Parmesan, if desired.