Preheat the oven to 450°F (230°C).
Toss the broccoli florets with the olive oil, cayenne, garlic powder, and a large pinch each of kosher salt and black pepper on a rimmed baking sheet.
Roast the broccoli for 15 to 20 minutes, tossing once, until edges are lightly charred.
Meanwhile, bring a large pot of salted water to a boil and cook the fettuccine until al dente according to package directions.
Reserve 1 cup of the pasta cooking water, then drain the pasta and return it to the pot.
Add the hummus, about 1/2 cup of the reserved pasta water, lemon zest, lemon juice, butter, and 3/4 cup grated Parmesan to the pasta.
Toss vigorously until a creamy sauce forms, adding more reserved pasta water a little at a time to reach the desired consistency.
Stir in the chopped basil, chopped parsley, and crushed red-pepper flakes, then taste and adjust seasoning with salt and black pepper as needed.
Add the roasted broccoli to the pasta and toss gently to combine.
Serve immediately with extra Parmesan and additional basil or parsley if desired.
