In another large frying pan, sauté onions in remaining oil on medium heat until softened. Add garlic, herbs, rice, and remaining ½ teaspoon salt, stirring for 1 minute. Add wine, stirring until wine has almost evaporated. Stir in 1 cup of broth, and add mushroom and cheese at the same time. Continue to add remaining broth, 1 cup at a time, as previous broth is absorbed into the rice.