Lightly season chicken with salt and pepper. Return Dutch oven to medium-high heat. Add 1 tablespoon bacon fat and heat until just smoking. Add half of the chicken, in a single layer, and cook until lightly browned, about 2 minutes per side. Transfer cooked chicken to a plate. Add remaining 1 tablespoon bacon fat and heat until just smoking, and repeat with remaining chicken.
Melt 3 tablespoons butter in now-empty Dutch oven over medium-high heat. When foaming subsides, add pearl onions and mushrooms and cook, stirring occasionally, until lightly browned, 5 to 8 minutes. Reduce heat to medium, add garlic and cook until fragrant, about 30 seconds. Add tomato paste and flour and cook, stirring frequently, until well-combined, about 1 minute.
Add reduced wine mixture, scraping bottom of pot with a spoon to loosen browned bits. Add 1/4 teaspoon pepper, cooked chicken (and any accumulated juices) and cooked bacon. Increase heat to high and bring to a boil. Reduce heat to medium-low, cover pot and simmer until chicken is tender, about 25 minutes, stirring halfway through cooking time.
Using a slotted spoon, transfer chicken to a large bowl and tent with aluminum foil to keep warm. Increase heat to medium-high and simmer until sauce is thick and glossy and measures about 3 1/2 cups, about 5 minutes. Remove from heat, stir in remaining 2 tablespoons butter and reserved 1 tablespoon wine. Season to taste with salt and pepper. Return chicken to pot. Top with minced parsley and serve immediately.
Nutrition information per each of 6 servings:
Calories530Fat32 gSodium300 mg