Prepare the Chicken - Trim any excess skin and fat from the chicken thighs. Dry the surface with a paper towel. Generously season with salt and pepper on both sides.
Sear the Chicken - Heat a large skillet or Dutch oven over medium heat. Melt the butter, then add the chicken. Sear each side until golden brown, about 4 to 5 minutes. Transfer to a plate.
Cook the Aromatics - Add the onions and saute until translucent, about 2 minutes. Add the garlic, and saute until fragrant, 30 seconds. Add the mushrooms, ½ teaspoon salt, and ¼ teaspoon pepper. Saute until tender, about 2 minutes.
Make the Sauce - Add the flour, stir, and cook for 1 minute. Add the wine and stir to deglaze, scraping the bottom of the pan to remove the browned bits. Stir in the chicken stock, ½ teaspoon salt, and ¼ teaspoon pepper. Bring to a boil over medium-high heat, and cook until lightly thickened, about 2 to 3 minutes.
Braise the Chicken - Add the chicken, skin side up to the pan. Add the thyme and bay leaf. Cover and simmer over low heat until the chicken reaches 170ºF (77ºC) on a meat thermometer, about 25 to 30 minutes.
Reduce the Sauce - Transfer the chicken to a clean plate and cover to keep warm. Discard the sprig and bay leaf. Bring the stock to a boil over medium-high heat, reducing to thicken, about 5 to 10 minutes.
Add the Cream - Stir in the cream and nutmeg. Simmer over medium heat until the sauce thickens, about 5 minutes. Taste and season with salt and pepper.
To Serve - Add the chicken back to the pan to warm for about 5 minutes. Garnish with parsley and serve hot.
Notes
Storing: Refrigerate in an airtight container for up to 5 days.
Reheating: Microwave on high setting in 30-second increments until hot. Alternatively, cook in a pan over medium heat until hot.
Make it Gluten-Free: Combine 2 tablespoons cornstarch with 1/4 cup of water. Add after reducing the stock, and cook until thickened, about 1 minute.