In a small saucepan, bring water to a boil, add pearl onions and reduce to a simmer for 10 minutes. Drain, cut off the root ends and slip off the skins.
In a Dutch oven or large heavy-bottomed pot, melt two tablespoons of butter over medium heat. Cook chopped bacon and pearl onions until the bacon turns crisp. Transfer the bacon and pearl onions to a plate with a slotted spoon and drain. Some chopped bacon pieces might finish cooking before others. Go ahead and transfer those as they're ready to prevent burning.
While the bacon cooks, season the chicken with salt and pepper and dust with flour. Once you transfer all the bacon and pearl onions, place the chicken skin-side down in the rendered bacon fat and butter. Cook undisturbed until the skin browns, about five to seven minutes. Flip and cook for another five minutes. You'll likely have to do this in two batches because you don't want to overcrowd the pan during browning.
Remove the last batch of chicken and whisk in 3 tablespoons of flour. Continuously whisk for about three to four minutes.
Slowly pour in the wine, brandy and Better Than Bouillon and continue to whisk until the flour smoothly incorporates with the liquids. Add the parsley, thyme, rosemary, bay leaves and garlic cut-side down.
Return the chicken, bacon and pearl onions to the pot. Bring to a boil and then reduce to a simmer and cover. Stir occasionally. Simmer covered for 45 minutes.
While the chicken braises, melt the remaining two tablespoons of butter in a pan. Add the mushrooms and cook until golden. During the final minutes of braising, add the mushrooms to the pot. You can cook the mushrooms ahead of time.
After the 45 minutes are up, add the mushrooms and simmer uncovered for another 15 minutes. Serve over buttered egg noodles, mashed potatoes or polenta. Enjoy!