Pat the chicken dry with paper towels. Season both sides of the chicken with the chicken seasoning.

Heat the olive oil and 2 tablespoons of butter in a large Dutch oven or braising dish over medium heat. Place the chicken skin side down and brown for about 3 minutes. Flip the chicken and cook for an additional 3 minutes.

Remove the chicken from the pan and set aside.

Add the carrots, onions, and apples to the pan. Cover with the lid slightly cracked and cook for about 10 minutes, stirring halfway through the cooking time.

Season the vegetables with 2 teaspoons of salt and 1/2 teaspoon of black pepper.

Make a well in the center of the vegetables and add 2 tablespoons of butter. Once the butter has melted, sprinkle the gluten-free flour over the vegetables. Stir to coat the vegetables and incorporate the flour.

Pour in the chicken broth and stir to combine. Taste the broth and adjust the seasoning with additional salt and pepper if needed.

Pour half of the pepper jelly sauce over the vegetables and stir to combine.

Place the chicken on top of the vegetables with the skin side facing up. Pour the remaining sauce over the chicken.

Cover the Dutch oven or braising dish and bake for 2 1/2 hours, or until the chicken is tender and cooked through.

Serve the braised chicken and vegetables over rice.