Pat the chicken pieces dry with paper towels. Season evenly on all sides with the kosher salt and black pepper.

Heat the olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat.

Place the chicken pieces in the pot skin-side down. Sear for 5 to 7 minutes until crisp and golden brown, then flip and brown the other side for 3 to 4 minutes. Remove the chicken to a plate and set aside.

Add the diced onion, carrots, bell peppers, and sliced mushrooms to the same pot. Sauté for 5 to 7 minutes until the vegetables have softened.

Stir in the minced garlic and cook for 1 minute until fragrant.

Pour in the wine to deglaze the pot, scraping up any browned bits from the bottom with a wooden spoon. Allow the wine to simmer and reduce by half, about 2 minutes.

Add the diced tomatoes with their juices and the kalamata olives. Stir well to combine the vegetable sauce.

Return the browned chicken pieces to the pot, nestling them gently into the sauce.

Bring the mixture to a gentle simmer, cover the pot, and reduce the heat to low. Braise for 35 to 40 minutes, or until the chicken is tender and cooked through (reaching an internal temperature of 165°F).

Remove the pot from the heat. Stir in the chopped fresh basil and fresh parsley. Serve hot over pasta, creamy polenta, or alongside crusty bread.