Place chicken breast on cutting board. Use a sharp knife to slice through horizontally, to form 4 evenly sized filets. Sprinkle both sides with 1 teaspoon of kosher salt and 1/2 teaspoon pepper and press to adhere.

Heat oil in a large pan over medium heat. Once the oil is shimmering, sear each side until golden and the chicken lifts from the pan easily, about 5-6 minutes. Place seared chicken aside on a plate and loosely tent with foil. Note: chicken will not be entirely cooked through yet.

In the same pan, add 1 tablespoon butter. Once melted, add the mushrooms, and remaining 1/2 teaspoon of both kosher salt and pepper and saute until they begin to soften, about 5 minutes. Place on the chicken plate.

Add remaining tablespoon of butter to the pan. Once melted, add the shallot and saute until it begins to soften, about 3-5 minutes. Add the champagne to the pan and bring to a simmer. Use the back of your spoon to scrape up any brown bits from the bottom of your pan. Continue to simmer for 10 minutes without the lid on, so the champagne can reduce.

Add heavy cream and tarragon and bring sauce back to a simmer. Return chicken, mushrooms, and accumulated juices back to the pan. Continue to simmer until the chicken has reached an internal temp of 165 F. Sprinkle additional tarragon on top before serving, and enjoy!