One hour before cooking, rinse the chicken under cold water and pat dry with paper towels. Season each piece generously with salt and pepper. Leave it at room temperature for an hour to absorb the flavors.
Preheat your oven to 375°F . Melt butter in a large oven-safe skillet over medium heat. Place the chicken pieces skin-side down without crowding the pan. Cook for 10 minutes without flipping until the skin is golden brown and crispy. Flip the chicken and cook for another 10 minutes, then remove it from the pan and set aside.
Using the same skillet (don’t clean it!), sauté the sliced onions and garlic in the rendered chicken fat. Stir occasionally for 8–10 minutes until the onions are lightly caramelized.
Nestle the chicken back into the skillet on top of the onion mixture. Sprinkle chopped tarragon over the top. Pour in the white wine and chicken stock, bringing everything to a gentle simmer.
Transfer the skillet to the oven, cover with a lid or foil, and bake for 30 minutes. The chicken will get incredibly tender as it absorbs the delicious braising liquids.
Remove the chicken from the skillet again, keeping it warm under foil. Place the skillet back on the stove over medium heat. Stir in the heavy cream and simmer for 5–7 minutes until the sauce thickens. Deglaze the pan as you stir, scraping up all the browned bits for maximum flavor. Return the chicken to the skillet, coat it in the sauce, and cook for an additional 5 minutes.
Serve the chicken hot, garnished with additional fresh tarragon for a burst of color and flavor.