Warm the butter and oil in a large skillet over medium-high.
Add the onion and mushrooms and saute until they soften--about 5 minutes.
Add the rice to the skillet and stir, cooking for an additional 1-2 minutes. Then add 1 cup of the broth and stir until absorbed. Once absorbed, stir in another cup of broth and stir until it is absorbed. Repeat this process with the remaining cup of broth.