Season the chicken thighs with salt and pepper. Add 1 tablespoon of olive oil to the bacon grease in a large skillet or Dutch oven over medium-high heat. Brown the chicken on both sides (about 3–4 minutes per side). Remove and set aside.
Add the onion, carrots, and garlic to the pan. Sauté for 5 minutes until softened.
Pour in the red wine, scraping up any browned bits from the bottom of the pan. Bring to a simmer.
Return the chicken and bacon to the pan. Add the chicken stock, bay leaf, and thyme. Cover and simmer for 20 minutes over low heat.
In a separate skillet, heat the remaining olive oil. Sauté the mushrooms until browned and tender. Add to the simmering chicken.
In a small bowl, mash the butter and flour together to form a paste (beurre manié). Stir it into the sauce and let it simmer uncovered for another 5–10 minutes until the sauce thickens.
Remove the bay leaf and thyme sprigs. Garnish with fresh parsley and serve over mashed potatoes, rice, or crusty bread.