Add cognac and let burn down to about half (flambé if you are comfortable otherwise this works). Pour in the red wine and chicken stock. Add bacon, tomato paste, garlic, bay leaf and thyme sprigs. Stir enough to incorporate and move to oven, covered for one hour.

Meanwhile place cornstarch and soft butter in a small dish and stir with a fork until the cornstarch is incorporated into the butter. Set aside.

While chicken is cooking, bring water to a boil in a small pan. Drop pearl onions into the water and bring back to a boil. Let boil for 1 minute. Strain onions in a sieve and run cold water over them until cool enough to handle. Trim both ends of onion and gently remove the outer skin. In same pan, heat olive oil and add onions. Toss for several minutes until onions are browned. Add water to half way cover the onions, sprinkle with salt, and cover the pan with a lid. Slowly simmer for 30 minutes until fork tender. Reheat if necessary.

Heat butter and olive oil in larger pan. Add quartered mushrooms and toss for 5 minutes until a light golden brown. Reheat if necessary.

Return chicken to the Dutch oven to serve or arrange chicken on a platter; mushrooms on one side and pearl onions on the other. Drizzle with a little sauce and remaining sauce on the side.