In a heavy large deep pot, sauté the bacon over medium high heat in 2 tablespoons oil until lightly browned, about 2 minutes. Transfer the bacon to a separate dish. Make sure to keep the yummy drippings in the pan.
Season the chicken generously with salt and pepper. With the drippings in the pot, keep your stove at medium high heat. Add the chicken. If you’re doubling the recipe, you may need to use 2 pots for this, so you don’t crowd the pan. If the chicken is crowded, it won’t get that gorgeous caramelized brown color.
Turn the chicken until it’s nicely browned on both sides. Carefully and slowly pour the Cognac into the pan. It should bubble up around the meat. The next step may seem daunting (and it’s totally not necessary), but if you’ve been watching a lot of Top Chef lately and are feeling extra “chef like”, take a long lighter and light the Cognac. It will flame up and you can tilt the pan around for a bit. Your friends and family will be extremely impressed! Let it flame for a couple of minutes, then cover the pot with the lid to put the flame out.
Add the bay leaf, thyme, onions and carrots to the pot. Cover and simmer gently, turning the chicken once, for about 10 minutes. At this point your kitchen will be filled with the gorgeous smells of a French bistro.
Uncover the pot, sprinkle the flour as evenly as you can over everything. With tongs, turn the chicken around to help lightly coat it with the flour. Cover and cook, turning the chicken once or twice more, for 3 to 4 minutes.
Remove the pot from the heat and gradually stir in the wine and enough stock to almost cover the chicken.
Put the pot back on the stove; add the bacon, garlic, tomato paste, and mushrooms to the pan. Cover, and gently simmer for 25 to 30 minutes. Test the chicken for doneness. There should be no trace of pink and the juices should run clear when the meat is pierced with a knife.
The sauce should be just thick enough to lightly coat the chicken and vegetables. If it is too thin, turn the heat up to bring the sauce to a boil. Boiling for about 3-5 minutes should thicken the sauce. If the sauce is too thick, thin it with an extra 1/4 cup of chicken broth. Season to taste with extra salt and pepper.
Serve immediately or let cool, cover, and refrigerate overnight. To reheat, skim any fat that has congealed on the surface of the stew and reheat it over medium high heat.