Take the goat chops and use your knife to score the fat cap in a crosshatch pattern, making shallow cuts across the surface. This helps the fat render better during cooking.
Season all sides of the chops generously with kosher salt and black pepper, then sprinkle with the finely chopped rosemary, pressing it gently into the meat. Place the seasoned chops on a plate or baking sheet and put them in the refrigerator, uncovered, for at least 2 hours or up to 24 hours. This dry brining step is crucial for flavor and texture.
When you're ready to cook, take the chops out of the refrigerator and let them sit at room temperature for 30 minutes. This ensures even cooking.
While waiting, gather your cast iron skillet and other ingredients. Pat the chops dry with paper towels if you see any moisture on the surface.
Place your cold cast iron skillet on the stove and add the olive oil. Place the goat chops fat-side down in the cold pan, then turn the heat to medium. This slow start helps render the fat better.
Cook the chops on the fat side for 2-3 minutes until golden brown. You'll see the fat starting to melt and turn crispy.
Turn the heat up to high, then flip the chops onto one of their flat sides. Cook for 2 minutes.
Flip the chops to the other flat side and cook for another 2 minutes. If you're using a meat thermometer, start checking the temperature now.
Add the butter, crushed garlic cloves, and a sprig of rosemary to the pan. As the butter melts, tilt the pan slightly and use a spoon to baste the chops with the hot butter for about 30 seconds.
Check the internal temperature with your meat thermometer if using one. For medium-rare, look for 130°F (54°C). For medium, aim for 135°F (57°C).
Transfer the chops to a plate lined with paper towels and let them rest in a warm spot for 4-5 minutes. The temperature will rise another 5 degrees while resting.
Sprinkle with a little flaky sea salt and serve with lemon wedges on the side. Don't forget to pick up the bones with your hands after cutting off the meat – that's where some of the best bites are hiding.
If you want to save the chops for later, let them cool completely, then store in an airtight container in the refrigerator for up to 3 to 4 days. Reheat them gently in a low-temperature oven (300°F/150°C) for about 10 minutes to avoid toughening the meat.