Sear the Chicken:
Pat the chicken dry and season with salt and pepper. Heat butter and olive oil in a Dutch oven or deep skillet over medium-high heat. Brown chicken on both sides (about 4–5 minutes per side), then transfer to a plate.
Sauté the Vegetables:
In the same pan, add onion, carrots, and celery. Sauté for 5–6 minutes until softened. Add garlic and cook for another 30 seconds.
Add Flour:
Sprinkle in the flour and stir for 1–2 minutes to coat the vegetables and cook out the raw flour taste.
Deglaze and Simmer:
Slowly pour in the white wine, scraping up any browned bits. Then add chicken broth, thyme, and bay leaf. Stir until smooth and slightly thickened.
Return Chicken to the Pan:
Nestle chicken pieces back into the sauce. Reduce heat to low, cover, and simmer for 25–30 minutes, or until chicken is cooked through and tender.
Finish the Sauce:
Stir in the cream and simmer uncovered for another 5–10 minutes, until the sauce is rich and slightly thickened. Add lemon juice for brightness if desired.
Serve:
Remove bay leaf. Garnish with chopped parsley and serve hot with mashed potatoes, rice, or crusty bread.