Bring chicken broth and water to boiling in a large pot. Add the pasta and cook according to package directions. Four minutes before the pasta is finished add the broccoli to the pot. Just before draining, reserve 1 cup of the cooking liquid. Drain and return the pasta and broccoli to the pot.
While the pasta is cooking, heat the olive oil in a large skillet over medium-high heat. Saute the sausage slices until lightly browned, 2 to 3 minutes.
Add the sausage and any olive oil in the pan to the drained pasta mixture. Stir in the lemon peel, lemon juice, salt, and enough of the reserved cooking liquid to moisten. Serve topped with cheese. Makes 4 servings.