Preheat oven to 400°F.
Toss carrots and Brussels sprouts OR broccoli with olive oil. Season with salt and pepper and spread evenly on a large parchment-lined baking dish. Place in the oven and roast for 25-30 minutes, tossing halfway, until browned and tender.
While vegetables are roasting, cook pasta according to package directions. Drain, reserving a 1/2 cup of the starchy pasta water, and set aside.
While pasta and vegetables are cooking, place basil, spinach, lemon juice [to taste], walnuts, nutritional yeast, and garlic in a food processor. Blend until finely chopped, drizzling in the olive oil until pesto is pureed to your desired texture preference. Season with salt and pepper to taste.
Combine cooked pasta with roasted vegetables and about 1/3 cup pesto [or more] with enough reserved starchy pasta water to form a sauce thickness of your preference.
Then serve garnished with parmesan [if using] and 1-2 leaves of basil.
The pesto freezes beautifully. Consider saving the rest of the pesto for other purposes by packaging it in baby jars and freezing it for up to 1 month.
Also feel free to sub a bag of frozen vegetables of choice for the carrots + Brussels or broccoli to save on time. Simply pan fry the frozen veg in olive oil + sea salt and add into pasta as you would in step 5.