Pat chicken dry with paper towels and season liberally with Kosher salt and pepper. Let sit for at least 10 minutes. Meanwhile, heat oven to 400 degrees.
Heat one tablespoon of butter in a 12-inch non-stick skillet over medium high heat. When butter just begins to brown, add chicken breasts to skillet and sear for 4-6 minutes until you have a nice brown crust.
While chicken is browning, melt remaining tablespoon of butter to a 13 x 9 inch baking pan placed in the oven. Once chicken is browned on one side, add to baking pan, browned side up, and bake until chicken reaches 160 degrees, about 15 minutes. Let chicken rest for about 5 minutes before serving.