Cook pasta in a pot of generously salted boiling water 2 minutes less than per package instructions.
Reserve 1 cup pasta water and cover to keep warm. Add broccoli to pot; continue boiling until pasta is al dente and broccoli is bright green, 1 to 2 minutes more. Drain.
Return pot to medium heat; add cream cheese, butter, and ⅔ cup reserved pasta water. Cook, stirring, until mixture is smooth and simmering.
Remove from heat; stir in pasta, broccoli, and Parmigiano-Reggiano. Toss with more pasta water as needed until sauce clings to pasta. Serve with more Parmigiano and black pepper.
