Preheat the oven to 350°F (175°C). Pat the chicken dry with paper towels and season all sides generously with salt and pepper. In a large, deep oven-safe skillet or Dutch oven, heat the olive oil over medium-high heat. Sear the chicken for approximately 4 minutes per side until a golden-brown crust forms. Transfer the partially cooked chicken to a separate plate.

Remove excess fat from the pan, leaving about one tablespoon. Melt the butter in the same pan, then add the chopped onion and carrot. Sauté over low heat for 7 to 10 minutes until softened. Stir in the garlic and thyme, allowing them to cook for an additional 30 seconds until fragrant.

Sprinkle the flour evenly into the pan and stir thoroughly to create a roux. Cook for 1 to 2 minutes until the mixture emits a light, nutty aroma. Pour in the white wine, scraping the pan to deglaze. Let it simmer briefly to reduce slightly, then incorporate the chicken stock, stirring until fully blended.

Return the browned chicken and any accumulated juices to the pan, nestling the pieces into the sauce. Transfer the pan to the preheated oven and bake, uncovered, for 45 minutes or until the chicken is tender and thoroughly cooked.

Carefully remove the pan from the oven. Stir in the heavy cream and adjust the seasoning with additional salt if needed. Mix until the sauce is smooth and uniformly creamy. Serve immediately alongside your choice of side.