||Remove skin from chicken if desired. Season chicken with thyme, salt and pepper.
||Heat a large covered skillet over medium heat. Add olive oil (if skin removed); brown thighs 5 minutes per side. Remove from pan. Drain excess fat.
||Add mushrooms and shallots. Cook 5-7 minutes, stirring occasionally until softened.
||Add tomato, 1/2 cup broth and wine. Bring to a simmer, stirring to scrape up browned bits from bottom of pan. Return chicken and any juices to pan. Reduce heat, cover and simmer 20 minutes until chicken is cooked through (180°F).
||Remove chicken and keep warm, reserving mushrooms in pan. Add remaining 1/4 cup broth if liquid has evaporated. Stir in parsley; increase heat and simmer 1 minute until sauce is slightly reduced and thickened. Place a chicken thigh on a serving of polenta or potatoes and surround with mushrooms and sauce.