Cook Bacon: Add the olive oil to a large dutch oven over medium heat. Add the bacon, and cook until crisp, 5-7 minutes. Remove the bacon with a slotted spoon and set it aside, leaving the fat in the pot.
Cook Chicken: Season the chicken thighs with salt and pepper. Increase heat to medium-high and place the chicken, skin down, in the pot. Cook until the skin is crisped and golden brown, remove the chicken from the pot and set it aside.
Add Ingredients: Reduce the heat to medium and add the onion and carrots. Cook for 4-5 minutes, or until the onion softens. Add the garlic and cook for 30 seconds before pouring in the cognac. Cook for 1 minute, then stir in the tomato paste. Continue cooking for another 30 seconds, then stir in the red wine, chicken broth, thyme, and bay leaves.
Cook: Bring the mixture to a boil, then reduce the heat to a simmer. Add the chicken back to the pot and nestle it into the liquid. Cover the pot with a lid and simmer for 20 minutes.
Cook Onions and Mushrooms: Meanwhile, in a separate skillet, melt 2 tbsp of butter over medium heat. Add the pearl onions and mushrooms. Cook for 10-12 minutes, stirring often, until nicely browned.
Make Sauce: Mix the remaining butter with the flour to create a paste. Remove the chicken from the pot and set it aside. Whisk the flour/butter mixture into the sauce and increase heat to medium-high. Whisk until it has thickened. Add the pearl onions and mushrooms to the pot and simmer over medium heat for 5 minutes.
Optional Broil: While the sauce simmers, place the chicken, skin-side-up, on a baking sheet. Broil for 2-5 minutes to crisp the skin.
Finish & Serve: Add the chicken and bacon back to the pot and garnish with freshly chopped parsley.