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Preheat oven to 400℉. Line a large rimmed baking sheet with parchment paper. Add the cauliflower, butternut squash, red bell pepper, broccoli, mushrooms, and shallots. Drizzle with the olive oil and sprinkle with the salt and pepper. Toss to coat. Arrange vegetables in a single, even layer (you may need to do this with 2 baking sheets if yours isn't large enough). Bake for 25-30 minutes, tossing once, or until vegetables are tender, caramelized, and golden brown.
While vegetables are roasting, make the pesto. Add broccoli florets to your food processor and pulse until very finely chopped. Add the basil, parsley, garlic, pine nuts, parmesan, lemon juice, salt, and pepper and pulse several more times. Add the olive oil and blend until smooth. Season to taste with additional salt and pepper if desired.
Bring a pot of water to a boil for the pasta and salt the water. Once boiling, add your pasta and cook according to package directions, or until just al dente. Remember to reserve your pasta water (I just scoop a bunch out with a large mug or heat-safe glass measuring cup!) Drain pasta, and add back into the pot or a large mixing bowl. Add the pesto and a splash (start with 1/4 cup) of the pasta water and stir to coat the pasta. Add the roasted vegetables, several cranks of freshly cracked black pepper, and a couple pinches of salt and stir to combine. Add a couple handfuls of parmesan cheese and another splash of pasta water if it seems like it needs more moisture. Season to taste with additional salt and pepper if needed. Serve with extra parmesan, basil leaves, and crushed red pepper flakes if desired.