Heat a large saucepan over medium-high heat and add the butter and oil. Add the bacon and sauté until crisp. Remove the bacon with a slotted spoon and set aside. Add the chicken to the hot pan and brown on all sides. Pour off the fat from the pan into a heatproof container and reserve.
Pour the brandy over the chicken in the pan. The brandy should flame; if it doesn’t, hold a lit match over the pan. When the flames die out, scrape up the browned bits and add the garlic, bay leaf, thyme, tomato, wine, stock, and bacon. Cover the pot, reduce the heat to medium low, and simmer until the chicken feels firm and its juices run clear when pierced, about 30 minutes. Remove the chicken from the pan, reserving the cooking liquid.
Meanwhile, in a medium sauté pan over medium-high heat, heat the reserved bacon fat. Sauté the mushrooms until lightly browned, about 10 minutes. Set aside.
Make the beurre manié—With a fork or in a food processor, cream the butter. Add the flour to make a smooth paste. Set aside.
Bring the liquid in the pan to a simmer and skim the surface. Continue to simmer until the liquid is reduced by half. Whisk in the beurre manié 1 Tbs. at a time until the liquid is the consistency of light cream (you may not need all the beurre manié). Add the mushrooms and simmer for 5 minutes. Taste and add salt and pepper if needed. To serve, ladle the sauce over the chicken.