Preheat the oven to 250℉ (120℃).
Fry the bacon in a large cast-iron skillet (mine is 12 inches) over moderately low heat. Cook until the bacon renders some of its fat, 6-8 minutes, or until lightly browned. Remove the bacon with a slotted spoon to a paper-towel-lined plate and set aside. Keep the pan hot.
Liberally sprinkle the chicken on both sides with salt and pepper. Brown the chicken pieces in batches in a single layer for about 5 minutes in the bacon grease, turning to brown evenly. Remove the chicken to the plate with the bacon and set aside. You’ll probably need to do this in batches.
Melt the butter with the fat that’s left in the pan, then add the carrots, sliced onions, salt, and pepper, and cook over medium heat for 10-12 minutes, stirring occasionally, until the onions are lightly browned.
Add the garlic and mushrooms, and cook for another minute. Sprinkle the flour over the vegetables and cook for 2-3 minutes while stirring constantly until the flour is paste-like.
Add the Cognac, bacon, chicken, and any juices that collected on the plate into the pot. Pour in the wine and chicken stock, add the thyme, and bring to a simmer.
Toss in the pearl onions, cover the pot with a tight-fitting lid, and place it in the oven for 30-40 minutes, or until the chicken is done and juices run clear, not pink.
Remove from the oven and serve with preferred sides.