Wash the zucchini thoroughly under cold water. Using a spiralizer or a vegetable peeler, create long, thin noodles from the zucchini. If you're using a spiralizer, follow the manufacturer's instructions.
In a dry skillet over medium heat, toast the pine nuts until they turn lightly golden and fragrant. This should take about 3-5 minutes, but be sure to watch them closely as they can burn quickly. Once toasted, set them aside to cool.
In a food processor or blender, combine the fresh basil leaves, toasted pine nuts, garlic cloves, and grated Parmesan cheese. Pulse a few times to break down the ingredients.
With the food processor or blender running, slowly drizzle in the olive oil until the mixture is smooth and well combined. You may need to stop and scrape down the sides of the container to ensure everything is incorporated evenly.
Taste the pesto and add salt and pepper to your liking. Remember that Parmesan cheese can be salty, so you might not need much additional salt.
In a large mixing bowl, toss the zucchini noodles with the freshly made pesto until they are evenly coated.
Divide the pesto-coated zucchini noodles among serving plates. If desired, garnish with halved cherry tomatoes for extra color and flavor.
Serve your Pesto Zucchini Noodles immediately as a light and flavorful meal. You can also refrigerate any leftovers in an airtight container for up to two days, though zucchini noodles tend to release water over time, so they're best enjoyed fresh.