Marinate the chicken pieces in the red wine with a sprig each of thyme and parsley, the bay leaves, and some salt and pepper for at least 2 hours, or overnight in the fridge.
Preheat your oven to 160°C (320°F).
In a large Dutch oven or oven-proof casserole dish, heat the olive oil and butter over medium heat. Add the chicken pieces (reserve the marinade), and brown them on all sides. Remove the chicken and set it aside.
In the same pan, add the chopped onions, carrots, and garlic. Sauté until the onions are translucent.
Sprinkle the flour over the vegetables and stir well until the flour is fully incorporated.
Gradually pour in the red wine marinade, stirring constantly until the mixture starts to thicken.
Add the chicken pieces back into the pan. Add enough chicken stock to cover the chicken. Bring to a simmer.
Cover the pan and place it in the preheated oven. Let it cook for about 1.5 hours.
While the chicken is cooking, in a separate pan, sauté the mushrooms and pearl onions in a bit of butter until golden.
After 1.5 hours, add the sautéed mushrooms and pearl onions to the casserole. Cook for another 30 minutes, or until the chicken is tender and the flavors are well combined.
Check the seasoning and adjust if necessary. Garnish with fresh parsley before serving.
Serve your Coq au Vin hot with mashed potatoes or crusty bread to enjoy the rich sauce.