Bring 5 cups water to a boil. Stir in rice, then reduce heat to low. Cover and let simmer for 40 minutes, or until rice begins to pop. Drain excess liquid from rice and set aside.
Melt 6 tablespoons butter in a large skillet over medium-high heat. Add the mushrooms and shallot and cook, stirring occasionally, until they have released their liquid and are golden brown, about 8 minutes.
Add white wine to deglaze the pan, and cook until most of the liquid has evaporated but mushrooms are still moist.
Mix mushrooms into prepared rice and season again with salt and pepper.