Start by prepping your squash “noodles.” I recommend using the medium blade on a spiralizer, but you can also use a julienne peeler, or shave the squash into ribbons with a vegetable peeler. Place the noodles in a colander in the sink and sprinkle with a good pinch of kosher salt. Toss gently, then let the noodles rest for 20 minutes. (This will help draw out excess moisture and soften the noodles.)
Meanwhile, make the pesto. Add the carrot tops and fresh basil leaves to the bowl of a food processor and pulse a few times until finely chopped. Add the garlic, walnuts, cheese, lemon juice, and good pinch of kosher salt and fresh ground pepper. Process until a coarse paste forms, scraping down the sides of the bowl a few times if necessary. With the motor running, drizzle in the olive oil. Transfer the pesto to a bowl and season with a little extra salt and pepper if necessary. (The pesto will be quite thick. That’s a good thing!)
Pat your noodles dry with paper towels and transfer them to a mixing bowl. Add about two-thirds of the pesto and toss to coat the noodles. (I recommend using kitchen tongs for this if you have them.) Feel free to add more pesto if you like, or save the remainder for another use.
Transfer the noodles to a serving dish or individual plates/bowls. Garnish with the shaved Parmesan, walnuts and fresh basil (if using), and serve.