Prepare the Chicken:

• Season the chicken: Sprinkle salt and pepper generously over the chicken thighs or breasts.
• Heat the butter and oil: In a large skillet, melt the butter with the olive oil over medium heat.
• Sear the chicken: Add the chicken, skin-side down, and cook for 5-7 minutes until golden brown. Flip and cook for another 3-4 minutes. Remove from the pan and set aside.

Cook the Aromatics:

• Sauté the shallots and garlic: In the same skillet, add the chopped shallots and garlic, cooking until softened and fragrant.

Deglaze the Pan:

• Add the white wine: Pour in the wine, scraping the bottom of the pan to release any browned bits. Simmer for 2-3 minutes to reduce slightly.

Make the Sauce:

• Incorporate the stock: Stir in the chicken stock and bring to a simmer.
• Add the cream: Stir in the double cream, mixing until smooth and well combined.

Finish the Dish:

• Return the chicken: Place the seared chicken back into the skillet, spooning the sauce over it.
• Add the tarragon: Sprinkle the chopped tarragon over the dish and simmer for 15-20 minutes, or until the chicken is cooked through.

Serve:

• Plate and garnish: Serve hot, garnished with extra tarragon leaves if desired.