Fill a large pot with lightly salted water and bring to a rolling boil over high heat. Stir in the broccoli, and cook, uncovered, for 3 minutes. Remove the broccoli with a slotted spoon; set aside. Stir the rotini into the same pot, and return to a boil. Cook uncovered, stirring occasionally, until the pasta is cooked through, but still firm to the bite, about 8 minutes. Drain.

Heat olive oil in a skillet over medium heat; cook and stir the garlic and crushed red pepper for 1 minute. Stir in the broccoli, chicken broth, lemon juice, salt, and black pepper. Bring to a boil; reduce the heat to medium-low and simmer until the broccoli is tender, about 5 minutes. Stir in the drained pasta; cook over low heat for 1 minute. Stir in the Parmesan cheese.