Preheat oven to 325°F.
Pat chops dry with a paper towel, and then generously sprinkle both sides with salt and pepper.
4 pork chops, Kosher salt and freshly ground black pepper
In a large skillet, heat the oil over medium-high heat.
2 tbsp olive oil
Add the chops and sear on one side for about 6 to 8 minutes, until golden brown on the bottoms. Flip the chops over and sear the other sides for another 6 to 8 minutes. The chops won't be completely cooked through at this point.
Transfer the chops and cook until the internal temperature reaches 135°F. An instant-read thermometer ensures the perfect temperature.
Meanwhile, pour all but about 1 tbsp of oil from the pan and reduce the heat to medium.
Add the shallots and sauté for 2 to 3 minutes, until soft. Stir in the garlic and sauté for another 30 seconds.
1 medium shallot, 3 cloves garlic
Add the capers and simmer for 1 minute.
⅓ cup capers
Add the vinegar, stock, and mustard and stir until combined. Simmer until slightly reduced, about 2 to 3 minutes.
2 tbsp Sherry vinegar, ½ cup chicken stock, 1 1/2 tbsp Dijon mustard
Stir in the cream and a healthy pinch of salt and pepper.
¼ cup heavy cream
Place chops on plate or platter and pour sauce over them. Pass remaining sauce at the table.