Pat chicken breasts dry. Cover breasts generously with kosher salt on both sides. Wrap in plastic wrap and place in the refrigerator for several hours or overnight to brine.
Preheat the oven to 350 degrees F (180 degrees C). Rub the inside of an oven-safe skillet with 1 tablespoon butter. Place chicken breasts in the skillet. Carefully pour the 1/4 cup of chicken stock around chicken, but not on top. Cover the skillet with heavy aluminum foil.
Bake in the preheated oven for 45 minutes, or until an instant read thermometer inserted in the hottest spot reaches 154 degrees F (68 degrees C). Remove chicken to a board and cut into bite-size pieces. Do not turn the oven off.
Place the skillet on the stovetop and bring to medium heat. Meanwhile, add remaining 3 cups stock to a saucepan and bring to a simmer.
Place cut chicken back in the skillet and saute until pieces are lightly browned, about 5 minutes. Remove and keep covered to stay warm.
Add remaining 3 tablespoons butter to the skillet, then add orzo. Stir for about 1 minute, then add the heated stock.
Return skillet to the oven and bake or until orzo is tender and starting to absorb the stock, about 30 minutes.
Remove the skillet and place it back on the stovetop. Bring to a medium-low heat, then stir in Parmesan. Add chicken back to the skillet; stir until sauce begins to thicken and chicken is completely warmed through.
Season with black pepper; serve in wide bowls with parsley garnish.
