Cook the pasta according to the package directions. Reserve 1 cup of the cooking water, drain the pasta, and return it to the pot.
Meanwhile, heat the oil in a skillet over medium-high heat. Add the garlic and cook, stirring, until golden, 1 to 2 minutes. Add the broccoli, red pepper, and 1 teaspoon salt. Cook until heated through, 1 to 2 minutes.
Add the broccoli mixture, lemon juice, Parmesan, and the reserved pasta water to the pasta. Cook over medium heat, stirring, until combined and heated through, 2 to 3 minutes. Sprinkle with the lemon zest and serve.