Preheat the oven to 450°F (232°C). Line a rimmed baking sheet with foil or parchment if desired.
On the baking sheet, toss the broccoli florets with the olive oil, cayenne, garlic powder, and a generous pinch each of kosher salt and freshly ground black pepper so they are evenly coated.
Roast the broccoli for 15 to 20 minutes, tossing once halfway through, until the edges are lightly charred and tender.
Meanwhile, bring a large pot of salted water to a boil. Cook the fettuccine until al dente according to package instructions, then reserve 1 cup of the pasta cooking water and drain the pasta.
Return the drained pasta to the pot. Add the hummus, about 1/2 cup of the reserved pasta water, lemon zest, lemon juice, butter, and grated Parmesan.
Toss the pasta vigorously until a creamy sauce forms, adding more reserved pasta water a little at a time to reach your desired consistency.
Stir in the chopped basil, parsley, and crushed red-pepper flakes. Taste and adjust seasoning with salt and freshly ground black pepper as needed.
Add the roasted broccoli to the pasta and toss gently to combine. Serve immediately with additional Parmesan and extra basil or parsley if desired.