Season chicken with 1 tsp salt and ½ tsp pepper. Dredge in flour and shake off excess.
Heat oil in a large (11–12 inch) sauté pan over medium-high until hot. Cook chicken skin-side down without disturbing until golden brown, 4 minutes. Flip and cook 4 more minutes. Remove and set aside.
Add pancetta and cook 1 minute. Add mushrooms, carrots, onion, thyme, and savory; cook stirring occasionally until vegetables begin to brown, 5 minutes. Add garlic and tomato paste; cook 30 seconds.
Add wine and bring to a boil, scraping up any browned bits. Add broth and stir. Nestle chicken skin-side up into the pan. Cover, reduce heat to medium-low, and cook 15 minutes.
Flip chicken and add pearl onions. Simmer 15 more minutes until chicken is cooked through. Uncover the last 5–10 minutes if you want a thicker sauce.
Season sauce with salt and pepper, skim off any fat from the surface, and serve over egg noodles or boiled new potatoes.