Pat the pork chops dry with paper towels and season on both sides with salt and pepper. Place a heavy saute pan over high heat. When the pan is hot, add the oil and 1 tablespoon butter to the pan and swirl to coat the pan evenly. Add the pork chop to the pan and sear for 2 to 3 minutes on the first side. The chops will turn golden brown as the natural sugars in the pork caramelize and create a nice crust. Turn the chops and sear on the second side for 1 minute. Transfer to the oven and cook to desired doneness. It should take about 10 to 12 minutes in the oven for the pork to be just cooked through and juicy.
Remove the pork from the oven and place the pork chops on a plate to rest while you make the sauce. Loosely cover with foil. Remove the excess fat from the pan and return the pan to the burner. Turn the heat to medium high. Carefully deglaze the pan with the sherry vinegar and sherry and scrape up the brown bits on the bottom of the pan with a wooden spoon. Add the veal stock and barbecue sauce and bring to a boil. Reduce the heat to a simmer and reduce until slightly thickened, about 4 minutes. Whisk in the Dijon mustard and the remaining 1 tablespoon butter and whisk to combine. Garnish with chopped tomatoes and minced chives.