Preheat the oven to 350°F. Pat the chicken dry with paper towels and season with salt and pepper. Heat the olive oil in a large, deep pan over medium-high heat. Brown the chicken for about 4 minutes on each side until golden brown, but not fully cooked. Remove the chicken and set it aside on a plate.
Discard excess fat from the pan, leaving about 1 tablespoon. Add the butter and sauté the chopped onion and carrots over low heat for 7-10 minutes until tender. Add the minced garlic and thyme leaves, cooking for another 30 seconds.
Stir in the flour, allowing it to absorb into the fat and cook until it releases a nutty aroma. Pour in the white wine and let it simmer, reducing slightly. Add the chicken stock and mix well.
Return the chicken to the pan, along with any juices. Place the pan in the oven, uncovered, and bake for 45 minutes.
Once the chicken is tender, remove the pan from the oven and stir in the heavy cream. Adjust seasoning with salt, if necessary, and stir until fully incorporated before serving.