Begin by gathering all the necessary ingredients. Allow the pork chops to sit at room temperature for approximately 30 minutes before cooking, ensuring an even cooking process.
If the chops have a fat cap, make a few vertical incisions to prevent them from curling during cooking.
Pat the pork chops dry using paper towels, then season both sides with kosher salt and freshly cracked black pepper.
Heat a 12-inch cast iron skillet over medium-high heat for about 3 minutes. Add vegetable oil to the pan. Once the oil is shimmering, place the pork chops in the skillet and sear for 2 minutes on each side.
Add the butter and sliced garlic to the skillet, stirring to combine.
Lay the sprigs of rosemary atop each chop. Tilt the skillet to allow the melted butter and oil to pool on one side.
Spoon the butter and garlic mixture over the chops occasionally, cooking for an additional 2 minutes. Remove the rosemary, turn the chops, and replace the rosemary on top. Continue to cook for an additional 2 to 3 minutes, basting the chops as needed. The pork should reach an internal temperature of 140°F (60°C) when tested with an instant-read thermometer.
Once the chops are cooked, remove them from the skillet and place them on a cutting board or serving platter.
Tent the chops with foil and allow them to rest for 5 minutes. During this time, the internal temperature will rise to 145°F (62°C).
Before serving, garnish the chops with freshly chopped rosemary.