Step 1

For the chicken:

Step 2

Place 1 chicken breast, skin side down, on cutting board, with ribs facing away from knife hand. Run tip of knife between breastbone and meat, working from thick end of breast toward thin end. Angling blade slightly and following rib cage, repeat the cutting motion several times to remove ribs and breastbone from breast. Find short remnant of wishbone along top edge of breast and run tip of knife along both sides of bone to separate it from meat. Remove tenderloin (reserve for another use) and trim excess fat, taking care not to cut into skin. Repeat with second breast.

Step 3

Using tip of paring knife, poke skin on each breast evenly 30 to 40 times. Turn breasts over and poke thickest half of each breast five to six times. Cover breasts with plastic wrap and pound thick ends gently with meat pounder until ½-inch thick. Evenly sprinkle each breast with 1/2 teaspoon kosher salt. Place breasts, skin side up, on wire rack set in rimmed baking sheet, cover loosely with plastic, and refrigerate for 1 hour or up to 8 hours.

Step 4

Pat breasts dry with paper towels and sprinkle each breast with ¼ teaspoon pepper. Pour oil in 12-inch skillet and swirl to coat. Place breasts, skin side down, in oil and place skillet over medium heat. Place heavy skillet or Dutch oven on top of breasts. Cook breasts until skin is beginning to brown and meat is beginning to turn opaque along edges, about 7 to 9 minutes.

Step 5

Remove weight and continue to cook until skin is well browned and very crispy, about 6 to 8 minutes. Flip breasts, reduce heat to medium-low, and cook until second side is lightly browned and meat registers 160 to 165 degrees, about 2 to 3 minutes. Transfer breasts to individual plates and let rest while preparing pan sauce.

Step 6

For the pan sauce:

Step 7

Pour off all but 2 teaspoons oil from skillet. Return skillet to medium heat and add shallot; cook, stirring occasionally, until shallot is softened, about 2 minutes. Add flour and cook, stirring constantly, for 30 seconds. Increase heat to medium-high, add broth and cherry pepper brine, and bring to simmer, scraping up any browned bits. Simmer until thickened, 2 to 3 minutes. Stir in any accumulated chicken juices; return to simmer and cook for 30 seconds. Remove skillet from heat and whisk in peppers, butter, and thyme; season with salt and pepper to taste. Spoon sauce around breasts and serve.