Preheat the oven to 450°F (230°C).
On a rimmed baking sheet, toss the broccoli florets with the olive oil, cayenne, garlic powder, and a generous pinch of kosher salt and freshly ground black pepper.
Roast the broccoli for 15 to 20 minutes, stirring or shaking the pan once, until the 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 off the heat.
Add the hummus, about 1/2 cup of the reserved pasta water, lemon zest, lemon juice, butter, and the grated Parmesan to the pasta.
Toss the pasta 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, parsley, and crushed red-pepper flakes, then taste and adjust seasoning with salt and 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.