In a saucepan, bring the broth and mushrooms to a boil, reduce the heat, and simmer for 10 minutes, or until the mushrooms soften. Remove the mushrooms; chop, and reserve for later. Keep the broth on low heat.
Saut� the onion and garlic for about 5 minutes or until tender. Add the rice and saut� 1 minute. Stir the wine into the rice mixture and simmer until the wine is absorbed.
Add the mushroom broth (1/2 cup at a time) while maintaining a simmer. The rice will absorb the broth mixture slowly and it is important to stir often.
When the rice has absorbed most of the broth (25 minutes) add the mushrooms and heat through. Continue to add the remaining broth slowly, stirring often. The rice will become creamy and the grains will be slightly firm in the center.
Serve immediately with cheese.