Preheat the oven to 350 degrees F.
Place a large pot or a Dutch oven over medium-high heat. Season the chicken pieces with salt and pepper. When the pot is hot, add the butter and olive oil. Place the chicken pieces into the pot, skin side down so that they fit snugly yet have room to color. Turn them after 2 minutes then cook for a further 2 minutes on the bottom. Remove the chicken to a plate. Add the bacon and cook until golden. Reduce the heat to medium, add the sliced onion, carrot and celery and cook for 2 minutes.
Blanch pearl onions in a 6 to 8-quart pot of boiling water 1 minute, then drain in a colander. When onions are cool enough to handle, peel. Set aside.
Next deglaze the bottom of the pot with 2 tablespoons of brandy. Stir all the ingredients well, lifting the browned bits off the bottom of the pot. While stirring, add the flour and cook for 1 minute. (This will create a roux and hold in all the flavors that have been created.)
Place the sprigs of thyme the pearl onions and the mushrooms into the pot and give them a stir, then return the chicken to the pot. Add the chicken stock and simmer for 5 minutes.
Add the red wine and the bay leaves; cover the pot and place into the preheated oven for 1 hour and 30 minutes, until the chicken is cooked through and quite tender.
Serve straight from the pot with Parsnip and Turnip Mash, if desired.