Preheat the Oven: Preheat your oven to 375°F (190°C).
Cook the Chicken: Melt the butter in a large pot over medium-high heat, then add the olive oil, garlic, and chicken. Stir until the chicken is golden, about 3 minutes.
Add Vegetables: Stir in the carrots and mushrooms, then sprinkle the flour over the top. Stir until it’s all combined with the chicken and vegetables. Cook for 5 minutes.
Add Liquids: Pour in the chicken stock and wine, stirring well. Let it cook and thicken for a few minutes.
Season and Thicken: Add salt, pepper, and fresh thyme. Stir in the cream and let the mixture bubble up and thicken, about 3 minutes. Turn off the heat.