Place the chicken and red wine in a zip-top bag and marinate overnight or for at least 4 hours.
Heat a large oven-safe skillet or dutch oven over medium-high heat with the olive oil. Remove the chicken from the wine, reserving the wine for the braise. Sear the chicken on all sides until browned. Remove the chicken from the pot.
Preheat the oven to 325°F.
Return the pot to medium heat with another tablespoon olive oil. Add the onion, celery, carrots, garlic, and bacon and cook, stirring, until the bacon is crisp and the vegetables are tender. Stir in the reserved wine, beef stock, thyme, mushrooms and chicken.
Cover the pot and place in the oven to braise for 45 minutes, until the chicken is tender.
Meanwhile, make the mashed potatoes. Coat the peeled garlic cloves in oil, wrap in foil and roast for about 20 minutes, until caramelized.
In a large stockpot, place the potatoes and a generous pinch of salt. Cover with cold water and bring to a simmer. Cook at a simmer until the potatoes are fork-tender, about 15 minutes. Drain the potatoes and return to the pot. Add the roasted garlic, butter, milk, buttermilk, salt and pepper. Mash until smooth.
To serve, divide the mashed potatoes and coq au vin between bowls. Sprinkle with parsley.