Prepare the vegetables. Chop the onion and peel and thinly slice the carrots. Place both in a small bowl and set aside.
Clean the mushrooms. Remove the stems and slice the mushrooms. Set aside.
Mince the two cloves of garlic and set aside.
Pat chicken with paper towels to dry.
Salt each side of the chicken.
Heat 1 tbsp of olive oil in a dutch oven.
Carefully lower the chicken pieces, skin side down, and cook for 3-4 minutes until golden brown. Turn the chicken over and cook an additional 3-4 minutes. The meat won't be cooked through, but that's fine; it will continue cooking later.
Remove the chicken to a plate and set aside.
Add the pancetta to the dutch oven and cook over medium-high heat until brown, about 5 minutes. Lower the temperature to medium heat if you notice the edges burning.
Remove the pancetta from the pot using a slotted spoon and allow to drain on a plate lined with paper towels. Set aside.
Pour off all but about 2 tbsp of fat from the pot.
Add the onions and carrots to the pot and cook over medium high heat until the onions are translucent and the carrots soft, about 7-8 minutes.
Sprinkle the dried thyme over the veggies and add the minced garlic. Cook for about 1 minute.
Carefully pour in the red wine and the chicken broth and stir.
Stir in one tablespoon of tomato paste.
At this point you can add in the mushroom slices or you can cook them separately. This step isn't necessary, but I prefer mushrooms cooked in butter. See Tips & Tricks for directions.
Add in the bay leaves and lightly salt to taste. NOTE: Remove the bay leaves before serving.
Return the chicken and the pancetta to the pot.
Cover the pot and allow to simmer over medium or low heat for 30 minutes. Do not allow the mixture to boil. The chicken is cooked when the internal temperature reaches 165 degrees F on an instant read thermometer inserted into the thickest part of the meat.