Dissolve 1 tablespoon of kosher salt in 2 cups of cold water in a medium bowl. Submerge chicken breasts and allow to brine for 30 minutes at room temperature.

Remove chicken from brine, rinse thoroughly under cold water, and pat completely dry with paper towels. Season with 1/4 teaspoon kosher salt and freshly ground black pepper on both sides.

Place your skillet over medium-high heat and add the oil. Heat until the oil shimmers but does not smoke (approximately 325-350°F).

Place chicken breasts presentation-side down in the hot skillet. Do not move them for 6-7 minutes to develop proper fond and Maillard browning.

After flipping, add 1 tablespoon butter to the pan, allowing it to melt around the chicken. Using a spoon, baste chicken with the butter 5-6 times. Continue cooking until internal temperature reaches 160°F at the thickest point (approximately 5-6 more minutes).

Transfer chicken to a plate and tent loosely with foil to rest.

Reduce heat to medium. Add shallots to the same pan and sauté until translucent (approximately 2 minutes). Add garlic and cook for 30 seconds until fragrant but not browned. Add thyme and rosemary sprigs.

Add apple cider to the pan, scraping up all fond from the bottom of the skillet. Increase heat to medium-high and reduce liquid by 2/3 (to approximately 2/3 cup), about 8-10 minutes.

Whisk in Dijon mustard. Remove herb sprigs. Reduce heat to low and whisk in heavy cream and remaining 1 tablespoon butter until emulsified. Taste and adjust seasoning with salt and pepper.

Slice chicken against the grain if desired, or serve whole. Pour sauce over chicken and garnish with fresh chives.