Use a julienne peeler, mandolin, or a spiralizer to cut the zucchini into noodles. Set aside.
Combine the basil and garlic in a food processor and pulse until coarsely chopped.
Slowly add the olive oil in a constant stream while the food processor is on.
Stop the machine and scrape down the sides of the food processor with a rubber spatula.
Add the lemon juice and Parmesan cheese or nutritional yeast.
Pulse until blended. Season with salt and pepper.
Combine the zucchini noodles and pesto.
Toss until zucchini noodles are well coated.
Top with tomatoes, if using. Serve at room temperature or chilled.