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Preheat oven to 325°F.
Pat chops dry with a paper towel, and then generously sprinkle both sides with salt and pepper.
In a large skillet, heat the oil over medium-high heat.
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.
Add the capers and simmer for 1 minute.
Add the vinegar, stock, and mustard and stir until combined. Simmer until slightly reduced, about 2 to 3 minutes.
Stir in the cream and a healthy pinch of salt and pepper.
Place chops on plate or platter and pour sauce over them. Pass remaining sauce at the table.