Synthesize the Pesto: In the bowl of a food processor, combine the ¼ cup of toasted pine nuts, nutritional yeast, lemon juice, garlic cloves, and ⅛ teaspoon of salt. Pulse several times until a coarse, sandy texture is achieved. Add the packed basil leaves and pulse again until the basil is finely chopped. With the processor running on low, stream in the extra-virgin olive oil until a smooth, vibrant green pesto forms. Scrape down the sides and set aside.
Prepare the Whole-Grain Pasta: Bring a large stockpot of water to a rolling boil. Do not salt the water. Add the whole wheat pasta and cook according to package directions until perfectly al dente. Before draining, carefully ladle out and reserve at least ½ cup of the starchy pasta water.
Cool and Lock Hydration: Drain the cooked pasta in a colander. Immediately spread the hot pasta in a single layer on a baking sheet. Drizzle with a teaspoon of olive oil and toss gently. This flash-cooling method prevents the pasta from becoming gummy and preserves its ideal texture. Let the pasta and the reserved pasta water cool to room temperature, about 15 minutes.
Prime the Vegetables: While the pasta cools, prepare your vegetables. Using a mandoline or a sharp knife, slice the zucchini and yellow squash into very thin rounds. Halve the cherry tomatoes. Rinse and drain the chickpeas thoroughly.
Unify the Ingredients: In a large mixing bowl, combine the cooled pasta, sliced zucchini and squash, halved cherry tomatoes, and drained chickpeas. Pour the prepared pesto over the top.
Emulsify and Season: Begin tossing the salad gently. Drizzle in half of the cooled, reserved pasta water to help the pesto coat every ingredient, creating a light, creamy sauce. Add the 2 tablespoons of lemon juice, ⅛ teaspoon of salt, and a generous amount of black pepper. Continue tossing, adding more pasta water a tablespoon at a time, until the salad reaches your desired consistency.
Garnish and Serve: Transfer the pasta salad to a serving platter. Garnish with the 2 tablespoons of toasted pine nuts, torn fresh basil leaves, and a pinch of red pepper flakes, if desired. Serve immediately at room temperature for the best flavor and texture.