1 whole chicken (3 1/2 to 4 pounds), cut into 10 pieces
Salt and pepper
1 pound brussels sprouts, trimmed and halved
2 medium shallots, thinly sliced
1 tablespoon Dijon mustard
1/4 cup cider vinegar
1/2 cup chicken broth
2 tablespoons heavy cream
Preheat oven to 375 degrees. In a large ovenproof skillet, heat oil over medium-high. Season chicken with salt and pepper. In batches, cook chicken until browned, about 6 minutes per side. Transfer to a plate, then add brussels sprouts and shallots to pan. Saute until golden brown, 3 minutes. Stir in mustard and cook 1 minute. Add vinegar and broth, return chicken to pan, and bring to a rapid simmer.
Transfer pan to oven and braise until chicken is cooked through, 20 to 25 minutes. Add cream to pan and swirl to combine; season with salt and pepper.