Place chicken breasts on a cutting board, cover with plastic wrap, and using a meat mallet thinly pound the chicken breast. Season each side of the chicken with a pinch of kosher salt and fresh ground black pepper. Pour the all purpose flour into a bowl, then proceed to coat each side of the chicken breast in flour. Shake the breast to get rid of excess flour, repeat with remaining chicken breast. 

Preheat oven to 400 degrees F

In a seasoned 10 or 12 inch cast iron skillet, over medium high heat on the stovetop, add 2 tbsp oil. Once shimmering, add the chicken breasts (depending on size you may need to do 2 at a time). Sear each side for about 2 minutes until a golden brown crust forms, remove and set aside (they will finish cooking in the oven).

Lower the heat to medium/low, add in 1/4 cup of white wine and deglaze the pan. Once the liquid has reduced by half, add in the butter, garlic, shallot, and fresh tarragon. Sauté for 3-4 minutes until butter has melted/shallots begin to turn translucent. Next, add in the chicken broth, dijon mustard, and lemon zest, whisk together until combined. Add in 1 tbsp of corn starch and whisk to combine, allow the sauce to come to a light boil, then reduce the heat to simmer. Give the sauce a taste and add a pinch of kosher salt and some fresh black pepper as needed.

Return the chicken breasts into the sauce, top with a few twigs of tarragon, and place into the oven for about 10 minutes. Cook time will vary depending on size of chicken breast and thickness, internal temperature should be 165 degrees F, use a digital thermometer to check. Remove from oven and serve with your favorite side, spooning sauce over the chicken.