Cut the ends off the zucchini. With a vegetable peeler, shave off as many thin slices as possible and transfer a large bowl. Repeat with the yellow squash and carrots.
Place the grape tomatoes between 2 large plates or tupperware lids. Press down, securing the tomatoes in place, and use a long, sharp knife to slice the tomatoes in half. Add to the bowl with the shaved vegetables.
Drizzle olive oil over the vegetables and season with salt and pepper. Toss to combine.
Make the pesto: Add the basil, parsley, cashews, garlic, salt, pepper, lemon juice, and olive oil to a food processor and process until smooth.
Spoon the pesto onto the shaved vegetables and mix well with tongs until fully coated and serve.