Rinse the mushrooms under cold water. Remove the base of the stem of the mushroom, and then wipe the remaining stem and cap with a clean, damp cloth (or paper towel ). Slice the mushrooms lengthwise into thin strips. (If using dried mushrooms, follow the package instructions to reconstitute them in water.)
In a large skillet over medium heat, melt the butter and add the onion. Cook until golden and then add the rice. Stir the rice for a couple of minutes until the butter is well absorbed. Heat the broth in a separate pan and keep warm. Add one ladle of the broth at a time, stirring constantly until absorbed. Repeat this process until all of the broth is absorbed, adding the mushrooms as described below.
In a another pan, heat the olive oil over medium heat, stir in the garlic and when golden add the sliced mushrooms. Saute the mushrooms over a medium-high heat for about 10 minutes. Add salt and pepper to taste, as well as some of the vegetable broth if necessary to keep moist. Remove from heat. Mix in the chopped parsley.
When the rice is about five minutes from done, add the mushrooms. Add the final ladle of broth and finish cooking together. Remove from heat and mix in the Parmigiano. Serve immediately with a sprinkle of Parmigiano and fresh ground pepper.