Pat the chicken legs dry with paper towels. Using a sharp knife, separate the drumsticks from the thighs. Remove any excess fat and skin from the thighs, and trim any veins from the thighs as well.

Place the 4 potatoes in a pot of water and cook until a skewer goes through easily. Remove from the water and let cool. Peel, cut into cubes, and brown them in a skillet with a little oil. Season with a bit of salt.

In a skillet, melt the butter with the olive oil. Brown the chicken pieces on both sides, then transfer them to a baking dish. Preheat the oven to 350°F (178°C).

In the same skillet, sauté the onion and garlic for a few seconds. Add the bell pepper, mushrooms, and carrots, and cook for 1 minute. Add the peas, wine, thyme, salt, and pepper, and cook for 2 minutes to let the alcohol evaporate.

Serve the chicken immediately with the vegetables and browned potatoes.