Preheat oven to its highest temperature (likely 450 degrees). In a small pot over medium heat, warm butter and salt until milk solids turn brown and it starts to smell nutty and rich, about 4 minutes. Turn off the heat and add bourbon very slowly. It will bubble up violently—don’t be alarmed. Keep warm until ready to use.
Place oysters on a bed of rock salt garnished with peppercorns in a cast-iron skillet. Cook until you see oyster juices just starting to bubble around the edges. Remove skillet from oven and pop open hot oysters, being careful not to burn yourself.
Place oysters on a serving platter or piece of slate covered in rock salt. Drizzle with warm bourbon brown butter. Garnish with a bit of country ham, lime zest, and a sprig of fresh cilantro. Serve while hot.