Heavily salt and pepper chicken pieces and place in a sealable plastic freezer bag. Add wine, bay leaf, thyme, and seal, pressing out air. Put aside for at least 2 hours or, preferably, refrigerate overnight.
Add bacon to Dutch oven and cook over medium heat to brown, about 10-15 minutes. Remove from heat and transfer cooked bacon pieces to a paper towel.
Remove chicken from bag and reserve marinade. Pat dry with paper towels, Working in batches, brown chicken pieces skin side down in hot bacon fat over medium-high heat, about 5 minutes per side. Transfer browned chicken pieces to a large plate.
Add onion, carrot, and ¼ tsp salt. Cook 7-8 minutes. Stir in garlic and tomato paste for 1 minute, add flour, and cook 1 more minute. Add wine marinade and reduce to 1½ cups, 12-15 minutes.
Add reserved chicken with accumulated juices to pot skin side up and partially submerge. Toss in half the cooked bacon. Cover pot and simmer over low heat for 1 hour. Remove cover and cook another 15 minutes to thicken slightly. Adjust seasonings if necessary.
While chicken is cooking, cook pearl onions and mushrooms, Add butter and oil to a frying pan over medium-high heat. Add pearl onions, sugar, and a pinch of salt. Cover pan and reduce heat to low. Cook for 15 minutes shaking pan occasionally to keep onions from sticking. Push onions to one side and add mushrooms. Continue cooking, stirring frequently until browned, 5-8 minutes. Transfer to a bowl and wipe down pan.
To make croutons, melt 2 tbsp butter with 1 tbsp olive oil in the same skillet over medium heat. When beginning to bubble, add bread triangles and crisp for 2 minutes on each side. Remove to a plate and lightly salt.
Transfer chicken pieces to a large serving bowl. Dip croutons in sauce and return to plate. Toss in parsley. Add onions, mushrooms, and remaining bacon to the sauce in the pot. Pour sauce with vegetables over the chicken. Sprinkle any remaining parsley on top. Garnish with croutons and serve.
To serve, transfer chicken to a large bowl, pour sauce over, and sprinkle with parsley,