Melt 3 tablespoons butter with 1 tablespoon oil in a large skillet over medium-high heat. Add onion, season with salt and pepper, and cook, stirring occasionally, until softened and lightly golden, 4-5 minutes. Add garlic and cook for 1 minute. Stir in wine and cook until liquid is reduced by half, about 2 minutes. Add remaining 3 tablespoons butter, remaining 1 tablespoon oil, and mushrooms. Cook, stirring occasionally, until mushrooms are lightly golden, about 5 minutes. Add cream and nutmeg and cook until slightly thickened, about 2 minutes. Stir in 1 teaspoon oregano. Season to taste with salt, pepper, and lemon juice. Toss in a skillet with cooked pasta, or serve over smashed boiled potatoes. Garnish with more oregano.