Melt 1 T. butter in heavy medium saucepan over medium saucepan over medium-high heat. Add zucchini, and cook until beginning to soften, stirring frequently, about 3 minutes. Transfer to bowl; reserve saucepan (do not clean).
Bring 3 cups broth to simmer in small saucepan. Reduce heat to lwo and keep warm.
Melt remaining 2 T. butter in reserved medium saucepan over medium-low heat. Add onion and cook until tender, stirring occasionally, about 6 minutes. Add rice and stir until opaque, about 2 minutes. Add 1/2 cup broth. Adjust heat so liquid simmers slowly and cook rice until broth is absorbed, stirring occasionally. Continue adding broth, 1/2 cup at a time, until rice is just tender and creamy, stirring occasionally, about 25 minutes.
Season with salt and pepper. Add zucchini and stir until heated through. Mix in cheese.