Cook the broccoli in boiling salted water until tender, 5 minutes; remove to a bowl with a slotted spoon. Add pasta to water and cook according to package directions; drain.

Process basil, garlic, oil, lemon zest, red pepper, and Parmesan in a food processer until finely chopped. Add broccoli and pulse until coarsely chopped, 4 to 6 times. Season with salt and black pepper.

Stir broccoli pesto and mascarpone into pasta until well coated; fold in chicken.