Prepare the Pork Chops: Pat the pork chops dry with a paper towel. Season both sides with salt and pepper. Lightly coat each side with flour, tapping off any excess.

Cook the Pork Chops: Heat olive oil in a large skillet over medium-high heat. Place the pork chops in the skillet, leaving space between them. Sear for 4-5 minutes on one side until golden brown, then flip to cook the other side to a similar color.

Check the Temperature: Insert a meat thermometer into the thickest part of a chop, near the bone. When it reads 145°F, the pork is cooked through. Remove the pork chops to a plate to rest; they will continue to cook slightly from residual heat.

Make the Sauce: Lower the heat to medium. Add the minced garlic to the skillet and sauté for 1-2 minutes until aromatic. Pour in the chicken stock, add lemon juice, and capers. Let the sauce come to a simmer, scraping up the flavorful browned bits from the bottom of the pan.

Finish the Sauce: Once the sauce begins to reduce and thicken slightly, turn off the heat. Stir in the butter until it melts and is fully integrated into the sauce.