Preheat oven to 350°F.
Heat 1 tablespoon oil in a large ovenproof Dutch oven over medium-high heat.
Season chicken with salt and pepper.
Cook chicken in batches until browned, 5-6 minutes per side.
Transfer to a plate and drain fat from pot.
Add bacon to pot; cook until rendered.
Drain all but 1 tablespoon fat from the pan.
Add carrots, celery, and onion; cook until onion is translucent, 7-8 minutes.
Stir in 1 cup wine and tomato paste; simmer for 2-3 minutes.
Add remaining 3 cups wine. Gently boil, stirring occasionally until wine is reduced by half, about 15-20 minutes.
Return chicken to pot.
Add broth.
Tie thyme and rosemary sprigs together; add to pot.
Bring to a boil and cover pot.
Transfer pot to oven and braise until chicken is tender, about 1 1/4 hours.
Meanwhile, heat 1 tablespoon oil in a large pot over medium-high heat.
Add mushrooms; sauté until browned, about 5 minutes.
Transfer chicken from sauce to pot with mushrooms; keep warm.
Simmer sauce over medium heat until reduced by 1/3, about 20 minutes.
Season with salt and pepper. Go lightly on the salt until you taste it.
Add mushrooms and chicken to sauce.