Season the chicken with salt and freshly ground black pepper and set aside. Fry the bacon in a large Dutch oven until crisp. Transfer to a paper towel-lined plate and drain all but 2 tablespoons of the fat from the pan.

Working in 2 batches to avoid over-crowding the pan, brown the chicken over medium-high heat, about 3 minutes per side. Transfer to a large platter and set aside. Drain the fat from the pan, reduce the heat to medium and add the olive oil.

Add the chopped onion and sauté until softened, 2 minutes. Add the garlic and continue cooking until the mixture is fragrant and just beginning to develop a golden color. Add the brandy, scrape up any browned bits from the bottom of the pan and cook for 1 minute.

Add the wine and bring the mixture to a rapid simmer. Cook, stirring occasionally, until the liquid is slightly reduced, 6 to 8 minutes.

Reduce the heat to medium-low, add the bay leaf and thyme sprigs and return the chicken to the pan. Cover and cook for 30 minutes, turning the pieces over once or twice to ensure even wine flavoring. Transfer the chicken to a serving platter.

Increase the heat on the wine sauce to medium-high and use a spoon to skim some of the fat from the top if necessary. Add the carrots, pearl onions and mushrooms and season to taste with salt and pepper. Cover and continue cooking until the vegetables are tender, 6 to 8 minutes, then add the reserved bacon.

Using your fingers, make a paste with the butter and flour and add the mixture to the wine sauce. Cook, stirring often, until the sauce has thickened to the consistency of a glaze. Return the chicken to the pan and, using tongs, turn each piece to glaze with the sauce.

Transfer the chicken to the serving platter, spoon the vegetables around it and top with the remaining sauce. Serve immediately.