Preheat the oven to 425°F (220°C). Line a large baking sheet with parchment paper.
Place the broccoli florets on the prepared baking sheet. In a small bowl, whisk together the olive oil, lemon juice, salt, and pepper. Pour this mixture over the broccoli, tossing to coat the florets evenly.
Arrange the broccoli in a single layer on the baking sheet and bake for 20–25 minutes or until slightly charred.
While the broccoli is roasting, bring a large pot of salted water to a boil. Add the cavatappi pasta and cook according to the package directions. Reserve 1 cup of the pasta water before draining the pasta.
To a large nonstick skillet over medium-low heat, add olive oil. Once hot, add the minced garlic and sauté for about 1 minute.
Reduce the heat to low. Then, add the ricotta cheese and Parmesan cheese to the skillet, stirring to combine. Stir continuously for 2–3 minutes, or until the cheese melts.
Add the lemon juice, kosher salt, black pepper, and crushed red pepper, stirring well.
Gradually stir in ½ cup of the reserved pasta water, mixing until the sauce is well combined. If you prefer a thinner sauce, add more pasta water as needed. (I added ½ cup more pasta water, for a total of 1 cup.)
Add the cooked pasta and roasted broccoli to the skillet, tossing to coat evenly with the sauce.
Garnish with parmesan cheese and crushed red pepper.