Preheat oven to 475º F, and bring a large pot of water to a boil on the stove.
On a parchment-lined baking sheet, toss the broccoli florets with 2 tablespoons olive oil, 3/4 teaspoon salt, and 1/8 teaspoon pepper, making sure the oil and seasonings are evenly distributed. (If you prefer, you can toss the ingredients together in a bowl and then dump the broccoli mixture out onto the baking sheet.) On a second parchment-lined baking sheet, repeat the process with the cauliflower florets, tossing them with 2 tablespoons olive oil, 3/4 teaspoons salt, and 1/8 teaspoon pepper. Make sure the vegetables are spread out evenly on the baking sheets, and not heaped on top of each other, so they roast properly rather than steaming.
Place cauliflower in the oven and roast for 5 minutes; then add broccoli to the oven. Roast for 5 minutes more, and then stir both cauliflower and broccoli and rotate sheet pans to promote even roasting. Continue roasting for about 10 more minutes (20 minutes total for cauliflower and 15 minutes total for broccoli), until the vegetables have developed some gorgeous roasted brown spots. Remove from oven and set briefly aside, keeping warm.
Meanwhile, as vegetables roast, cook pasta according to package directions. Before draining the pasta, carefully reserve about 1 cup of pasta cooking water.
In a large serving bowl, toss the roasted vegetables with the cooked pasta. Sprinkle the parmesan, lemon juice, garlic, and remaining 1/4 teaspoon salt evenly over the pasta mixture, stirring as you do so to make sure they are evenly distributed throughout the pasta and not concentrated in one spot. Loosen as desired with reserved pasta cooking water (we usually use about 1/2 - 3/4 cup). Taste and adjust the pasta water, lemon juice and salt as needed. Serve immediately.
Broccoli and cauliflower florets: To get this recipe on the table in 30 easy minutes, we suggest purchasing the pre-cut florets that you can now find in most grocery stores. (You may need to trim a few bigger florets to make sure they're all roughly the same size, which promotes even roasting.) However, if you prefer to buy whole heads of broccoli and cauliflower at the store or farm market, you'll need about 6 average stalks of broccoli and about 1 medium-large head of cauliflower to yield the 8 cups of each type of vegetable that you need for this recipe. Just add a few extra minutes onto the prep time (or see make-ahead tips below).
Parmesan Cheese: To make this pasta recipe truly vegetarian, be sure to select a parmesan cheese made with non-traditional enzyme alternatives from microbes or fermentation, rather than the traditional rennet.
Make-ahead steps: Even if you don't purchase pre-cut veggies, and prefer to purchase whole heads of cauliflower and broccoli, you can still take advantage of another make-ahead option: cut the broccoli and cauliflower into florets in advance when you have a little extra time. Store them in the refrigerator in a tightly sealed container or plastic bag, and they should keep nicely for a few days. In addition, you can juice the lemon and mince the garlic a few hours ahead or the night before, and store them, tightly wrapped, in the refrigerator.