Using a julienne peeler, mandolin, or spiralizer, spiralize the zucchini into noodles. Add noodles to a large bowl. You can also purchase pre-spiraled noodles.
Place your noodles on a paper towel and pat them dry. Remove as much excess water as possible.
Add basil, avocado, garlic, pine nuts, and lemon juice to a food processor and pulse for 20 seconds or until pesto is chopped. Add in water and process again until completely smooth.
Transfer to the bowl of zucchini noodles and toss until the noodles are well coated. Top with tomatoes and cheese.