To make the sauce, combine avocado, garlic, lemon juice, and basil in a food processor (or blender). Puree until all ingredients are combined and the sauce is smooth. Season with salt and pepper to taste. Set aside.
Use a mandoline to julienne the zucchini. If you don’t have a mandoline, you can simply slice the zucchini into thin strips by hand (essentially you are going for the size of linguine, or thinner if you prefer).
Heat a pot of water over high heat. Once the water begins to boil, add your zucchini pasta. Cook for one minute and then quickly remove the zucchini to a bowl of cold water to stop the cooking process (i.e. blanch your veggies!). Drain the zucchini and set aside.
In a medium saucepan, heat 1 tbsp of olive oil over medium heat. Add shrimp to the pan, season with salt and pepper, and cook until pink.
Add the shrimp, avocado sauce, and cherry tomatoes to the drained zucchini pasta. Mix until thoroughly combine and serve immediately.