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Pat the chicken dry with a paper towel. Season with salt, pepper, garlic powder and thyme. Set aside.
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In a large oven-safe pan / skillet, melt the butter over medium heat. Add the onions and cook, for 5 minutes, stirring frequently, until they start to brown around the edges. Add the coconut aminos, vinegar and 3 tbsp of the chicken broth (reserving the rest for later) and cook for 15-20 minutes, or until the onions are soft and browned. Transfer the onions to a plate / bowl and wipe down the pan.
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Add the gluten-free flour (or cassava flour) to a wide, shallow bowl. Dredge the chicken into the flour on both sides, until evenly coated. Shake off excess.
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Preheat the oven to 400F.
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Heat the remaining butter in the wiped down pan over medium-high heat. Add the chicken and cook for 3 minutes, or until golden-brown, then flip and cook for another 2-3 minutes, or until golden-brown. Transfer the chicken to a plate and set aside.
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Add the arrowroot starch to a bowl and very slowly pour and whisk in the reserved chicken broth to the skillet, heat on medium-low heat, whisking periodically as needed, and cook until the sauce thickens, about 1-2 minutes.
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Stir in the onions then nestle the chicken back into the skillet. Use a spoon to cover and baste the chicken with some sauce, then spoon each piece with some onions and sprinkle an even amount of cheese on each piece.
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Transfer the pan to the oven and bake until the chicken is cooked through, and the cheese is lightly browned and bubbly, about 8-12 minutes.
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Remove from the oven and garnish with a tiny bit of fresh herbs. Serve with sides.