Bring the vegetable broth to a simmer in a medium saucepan. Keep the broth warm over very low heat.
Meanwhile, add the olive oil, 1 tablespoon of butter, and the diced onion to a heavy large saucepan. Cook, stirring occasionally, for about 5 minutes over medium heat.
Add the mushrooms and garlic, and cook until all of the liquid evaporates and the mushrooms start to brown slightly (about 10 minutes).
Stir in the rice and let it toast for a few minutes. Add the wine and cook, stirring continuously, until fully absorbed.
Add 1 cup of the hot vegetable broth to the rice, and stir until the broth is absorbed. Continue adding broth, 1 cup at a time, stirring continuously, until the rice is just tender and the risotto is smooth and creamy (about 25-30 minutes).
Turn off the heat, and taste if your risotto needs salt.* Add some, if necessary. Stir in the remaining 3 tablespoons of butter and Parmesan cheese. Let rest for 5 minutes. Serve.