In a large saucepan, bring the broth, basil, garlic, and lemon zest to a boil over medium-high heat. Season with salt and pepper, to taste.
Add the pasta and broccoli; cover and cook for 10 minutes.
Discard the basil. Mix in the lemon juice and cheese. Turn off heat and cover with lid. Let the cheese melt.
Garnish with additional zest and cheese, if desired.