In a large saucepan cook the mushrooms, onion, and garlic in hot oil until onion is tender but not brown. Stir in the rice. Cook and stir for 5 minutes.
Meanwhile, in another saucepan bring the vegetable or chicken broth to a boil; reduce heat and simmer. Slowly add 1 cup of the broth to the rice mixture, stirring constantly. Continue to cook and stir until liquid is absorbed.
Add 1/2 cup broth and the asparagus or broccoli to rice mixture, stirring constantly. Continue to cook and stir until liquid is absorbed. Add 1 cup more of broth, 1/2 cup at a time, stirring constantly until the broth has been absorbed. This should take about 15 minutes. Stir in tomato, carrot, and the remaining 1/2 cup broth. Cook and stir until rice is slightly creamy and just tender. Stir in fontina or Muenster cheese, Parmesan cheese, and basil or parsley. If desired, garnish with some tomato slices. Serve immediately. Makes 4 main-dish servings.