Season chicken thighs with salt and pepper. Heat olive oil in a large Dutch oven or heavy pot over medium-high heat. Add chicken and cook until browned, about 4 minutes per side. Transfer to a plate.
Reduce heat to medium. Add butter and onion; cook until softened, about 4 minutes. Add garlic and mushrooms; cook until mushrooms release their liquid and start to brown, about 5 minutes.
Sprinkle flour over the vegetables and stir to coat. Cook for 1 minute.
Slowly pour in chicken broth and wine, stirring constantly to prevent lumps. Add thyme, salt, pepper, and bay leaf. Bring to a simmer.
Return chicken to the pot, nestling into the liquid. Cover and reduce heat to low. Simmer until chicken is tender and cooked through, about 30 minutes.
Discard bay leaf. Taste and adjust seasoning. Garnish with parsley before serving.
Tips
Serve over egg noodles, rice, or mashed potatoes to soak up the sauce.
For a thicker sauce, let it simmer uncovered for the last 10 minutes.
Leftovers can be refrigerated for up to 3 days or frozen for 2 months.