Pat chicken dry with paper towels, then season with salt and pepper.
Melt butter and olive oil in a heavy-bottomed pot or skillet over medium-high heat. Place the chicken thighs skin side down in the pan and cook for four to five minutes until golden brown. Remove the chicken from the skillet. Set aside.
Add mushrooms, onion, carrot, and celery. Leave to Cook for 5 minutes.
Stir in the minced garlic and cook for 30 seconds. Add flour and cook for 1 minute.
Add the wine and chicken stock. Stir well to deglaze the pan. Throw in the bay leaf and thyme.
Stir in the heavy cream and place the chicken skin-side up back into the sauce. Cover and leave to simmer on medium-low for 10 minutes.
Remove the lid and let it simmer for another 20 minutes. The chicken is cooked when the internal temperature reaches 75°C/167°F or slightly higher.
Sprinkle with parsley, and serve over mashed potato, cauliflower rice, or white rice.