In a medium saucepan cook broccoli, covered, in a large amount of boiling water for 8 to 10 minutes or until tender (follow package directions if using frozen broccoli). Drain well. Set aside 1 cup of cooked broccoli.
In a food processor or blender combine the remaining broccoli and 3/4 cup of the chicken broth. Cover and process or blend until smooth; set aside.
In the same saucepan melt butter. Stir in flour, lemon zest, salt, and pepper. Add 1 cup milk all at once. Cook and stir until slightly thickened and bubbly. Cook and stir 1 minute more.
Stir in the reserved broccoli, blended broccoli, and the remaining 3/4 cup broth. Stir in cheese. Cook and stir until heated through. If necessary, stir in additional milk to reach desired consistency. Season to taste with additional salt and pepper.