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 paper towel and pat them dry. Remove as much excess water as possible.
In a food processor, combine basil, avocado, garlic, pine nuts and lemon juice and pulse for 20 seconds. Add in water and process again until smooth.
Transfer to the bowl of zucchini noodles and toss until the noodles are well coated. Top with tomatoes and cheese.