Heat butter in a heavy-bottomed pan over medium heat until foamy; cook and stir shallots and garlic in the melted butter for 3 minutes. Add mushrooms and rosemary; stir to coat, 1 minute.
Pour 1/4 cup white wine into mushroom mixture; cook and stir until mushrooms are golden brown, 3 to 5 minutes. Increase heat to medium-high; add cream and 2 tablespoons white wine. Cook and stir until gravy is creamy and thick, about 5 minutes. Season with salt and pepper; sprinkle with Parmesan cheese.
