Place bacon in a large skillet and cook over medium-high heat, turning occasionally, until crisp, 2 to 3 minutes. Drain bacon slices on paper towels and set aside.
Reserve 1 tablespoon bacon grease in the skillet. Add butter and melt over medium heat. Stir in onions and saute until soft and translucent, 2 to 3 minutes. Add garlic and cook until fragrant, about 30 seconds. Add mushrooms and toss to thoroughly coat with the butter-onion-garlic mixture. Season with nutmeg and pepper and cook until browned, 4 to 5 minutes.
Combine chicken broth, balsamic vinegar, soy sauce, and cornstarch in a bowl and whisk until well combined. Stir into mushroom mixture, pour in heavy cream, stir in reserved bacon, and simmer until sauce is bubbly and thickened, about 2 minutes.
Adjust seasoning and serve immediately garnished with chopped parsley.