Preheat the oven to 400°F. Add the zucchini, mushrooms, bell pepper, and cherry tomatoes to a large baking sheet. Toss with olive oil, salt, and black pepper until evenly coated.
Spread the vegetables into a single layer and roast for 20–25 minutes, stirring once halfway through, until tender and lightly browned around the edges.
While the vegetables roast, bring a large pot of generously salted water to a boil. Cook the pasta according to the package directions until al dente.
While the pasta cooks, prepare the pesto. Add the basil, walnuts, garlic, nutritional yeast, lemon juice, salt, and black pepper to a food processor.
Pulse several times until the ingredients are finely chopped. With the processor running, slowly drizzle in the olive oil until the pesto reaches a thick but spoonable consistency.
Taste the pesto and adjust the salt, lemon juice, or black pepper as needed. For a thinner pesto, add another tablespoon or two of olive oil.
Before draining the pasta, reserve about ¼ cup of the cooking water. Drain the pasta well and return it to the warm pot.
Add the pesto and roasted vegetables to the pasta. Toss gently until the noodles are evenly coated and the vegetables are distributed throughout.
Add a splash of reserved pasta water if the pesto seems too thick. Continue tossing until the sauce becomes glossy and clings to the pasta.
Serve warm with fresh basil, vegan Parmesan, and an extra drizzle of olive oil if desired.