Pat the chicken pieces dry with paper towels and season all over with 1/2 teaspoon of salt and 1/4 teaspoon of pepper. Melt the butter in a large Dutch oven or heavy-bottomed pot over medium-high heat. Working in batches, place the chicken skin-side down and brown for 4 to 5 minutes until golden. Flip and cook for another minute. Transfer the chicken to a plate.
Reduce the heat to medium. Add the mushrooms, onion, thyme, and bay leaf to the pot. Cook, stirring occasionally, for 5 to 7 minutes, until the onions have softened and the mushrooms are lightly browned.
Stir in the minced garlic and cook for 30 seconds until fragrant. Sprinkle the flour over the vegetables and cook, stirring constantly, for 1 minute.
Pour in the white wine, scraping the bottom of the pot to release any browned bits. Let it bubble and reduce for about a minute. Gradually whisk in the chicken stock until the sauce is smooth. Season with the remaining 1/2 teaspoon of salt and 1/4 teaspoon of pepper.
Return the chicken pieces to the pot, skin-side up. Bring the liquid to a gentle simmer, then reduce the heat to low, cover, and cook for 15 minutes.
Uncover the pot and continue to simmer for another 20 to 25 minutes, or until the sauce has thickened slightly and the chicken is cooked through. The internal temperature of the chicken should reach 165°F (74°C) on an instant-read thermometer.
Carefully remove the chicken pieces and set them aside on a plate. Remove the thyme sprigs and bay leaf. Pour the heavy cream into the sauce and stir to combine. Bring to a simmer and cook for 2 to 3 minutes until the sauce is velvety.
Return the chicken to the pot to rewarm. Taste the sauce and adjust seasoning if needed. Serve hot, spooning the sauce and mushrooms over the chicken, and garnish with fresh parsley.