Cook pasta according to the package's instructions
In the meantime, place 1/2 of the basil in a food processor. Add pine nuts, Parmesan cheese, cloves of garlic, and 1/2 teaspoon Kosher salt and process or blend until the ingredients are finely chopped.
Scrape down the sides of the bowl and add the remaining 3 cups basil. Process until a paste has formed. Scrape down the sides of the bowl if needed.
With the food processor running, stream in 1/2 cup olive oil. Continue blending as needed until the olive oil is combined.
Drain the pasta and combine it with pesto. Mix thoroughly with the tomatoes and serve. Add mixed greens if desired.