Warm a glug of olive oil in a large skillet over medium heat (if using an electric skillet, heat it to 325°F). Add the diced bacon, and saute until the bacon browns and crisps -- about 5 minutes. Use a slotted spoon to transfer the bacon to the Dutch oven.
Tip the sliced onions into the skillet, season them with salt and pepper, and saute until the strands are lightly caramelized -- about 8 minutes. Add the garlic to the onions, and let cook for just 1 minute. Transfer the onions and garlic to the Dutch oven.
If the skillet looks dry, add more olive oil. Then add the carrots and the (optional) brandy. Use a long-handled match to ignite the brandy and burn off its alcohol. When flames have died, transfer the carrots to the Dutch oven.
Pat the chicken thighs dry with paper towels. Then season the chicken with salt and pepper. Add more oil to the skillet, if necessary. Add the thighs skin-side down, and cook until the skin is richly browned -- about 4 minutes. Then flip to brown the other side for just 2 minutes. Transfer the chicken to the Dutch oven.
Add more oil to the skillet if necessary. Then add the mushrooms. Saute until moisture evaporates, and the mushrooms color attractively -- 5-8 minutes. Tip the mushrooms into a bowl, and set aside.
Add the chicken stock and enough wine to the Dutch oven to barely cover ingredients. Stir in the thyme. Bring to a boil over high heat. Then cover the pot, lower the heat, and gently simmer for 55 minutes. Add the mushrooms, cover the pot, and simmer for 5 minutes.
Use a large slotted spoon to transfer the chicken and vegetables to a serving platter. Then return the liquid in the pot to a boil. Add the cornstarch solution, and whisk until thick and smooth -- 30 seconds to 1 minute. Taste carefully for seasonings, adding more salt and/or pepper if necessary. Ladle the wine sauce over the chicken and vegetables. Serve with roasted or mashed potatoes.
MAKE-AHEAD NOTE: After step #6, let the chicken and vegetables cool, uncovered, in the Dutch oven for up to 3 hours. Re-warm over low heat when ready to serve. Otherwise, let cool to room temperature, then refrigerate overnight.