In a medium saucepan bring broth to boiling. Reduce heat; simmer until needed. Meanwhile, in a large saucepan cook mushrooms, onion, and garlic in hot oil over medium heat about 5 minutes or until onion is tender. Add uncooked rice. Cook and stir about 5 minutes more or until rice is golden brown.
Slowly add 1 cup of the broth to the rice mixture, stirring constantly. Continue to cook and stir until liquid is absorbed. Add another 1/2 cup of the broth, the zucchini, and carrots to rice mixture, stirring constantly. Continue to cook and stir until liquid is absorbed. Add another 1 cup broth, 1/2 cup at a time, stirring constantly until the broth is absorbed. (This should take about 20 minutes.)
Stir the remaining 1/2 cup broth into rice mixture. Cook and stir until rice is slightly creamy and just tender. Stir in beans and Parmesan cheese; heat through. Sprinkle with parsley and additional cheese, if desired.