Preheat oven to 325F. In a large oven-safe skillet or dutch oven, melt 1/2 tablespoon butter and 1/2 tablespoon olive oil over medium-low heat. Add onions and stir occasionally until onions are a deep caramelized color, about 20-25 minutes.
Add garlic to onions and cook 1 minute until fragrant. Deglaze pan with white wine and bring to a simmer. Cook until mostly reduced. Transfer onions to a bowl and set aside.
Pat chicken thighs dry and season well with salt and pepper. Melt remaining 1 tablespoon butter and 1 tablespoon olive oil in same skillet over medium-high heat. Once pan is heated, add chicken thighs and sear on both sides 3-4 minutes until golden-brown.
Pour beef broth into pan and arrange onions and thyme sprigs around chicken, folding until combined.
Cover pan and transfer to preheated oven. Bake chicken at 325F 1 to 1-1/2 hours until chicken pulls away from bone easily with a fork.
Optionally, crisp up the skin on the chicken by transferring to a separate medium skillet over medium-high heat and searing skin-side down until crispy.
Nestle chicken back into pan with onions and top with cheese. Broil chicken 1 inch from heat 2-3 minutes until cheese is golden-brown. Serve chicken warm with French bread for dipping and enjoy!