Cut bacon into strips and saute over medium heat until light brown in a heavy bottomed, large casserole or dutch oven. Remove and set aside, leaving bacon fat in the pan.
Season chicken pieces with salt and pepper, add a few teaspoons of olive oil to the pan, if needed, and brown chicken on all sides. Return bacon to the pan with the chicken, cover and simmer for 10 minutes(skip this 10 minute cooking step if using boneless chicken).
Uncover pan, increase heat to medium-high, add cognac and flambe (or just reduce slightly until some of alcohol evaporates). Add red wine and reduce slightly. Reduce heat to low, add stock, stir in tomato paste, garlic, bay leaf, and thyme. Bring to a simmer, cover and simmer for about 25-30 minutes or until chicken is cooked through.
While the chicken is cooking, heat a teaspoon or two of olive oil in a medium sized skillet over medium-high, add the pearl onions and saute until browned. Add 1/4 to 1/3 cup of water to the pan (enough to cover the bottom and come up half way to onions), cover and steam them until tender, about 15-20 minutes, or until tender. Remove the cooked onions to a bowl.
Using the same medium skillet, heat a teaspoon or two of olive oil over medium-high heat and saute the mushrooms until light brown. Add the cooked mushrooms to the onion in the bowl and set aside.
When chicken is finished cooking, remove from pan and skim off excessive fat.
Make the beurre manié by creaming butter and flour together in small bowl. Heat the chicken cooking liquid over medium heat and beat the beurre manié into the liquid with a whisk. Simmer for a few minutes or until sauce is thickened.
Add chicken back to pan with the cooked onions and mushrooms. Stir well, taste and adjust seasonings, then simmer for a just few minutes to pull all flavors together and to heat everything through.
Adapted from Julia Child's classic recipe
Store leftover Coq au vin in a covered container in the refrigerator for up to 2 days