Dry the pork chops with paper towels. Sprinkle with brown sugar, onion powder, garlic powder, ground mustard, salt, and black pepper.
In a large cast iron skillet, heat the oil and butter over medium heat. You'll want the pan very hot, almost smoking before adding in the pork chops.
Brown the pork chops on each side. Use tongs to flip them. Preheat the oven to 350 degrees F and line a half sheet pan with aluminum foil. Work in batches until all of the pork chops are browned. Place the pork chops on the prepared sheet pan and place in the oven to continue cooking while you finish the remaining steps.
Add a few tablespoons additional butter to the hot skillet if more fat is needed. Add the sliced mushrooms and stir with a wooden spoon until browned, about 5-7 minutes. Once the mushrooms are browned, deglaze the pan with white wine and push the brown bits off the bottom of the skillet with the wooden spoon.
Dissolve the cornstarch in the cold water and stir with a spoon. Add the cornstarch mixture to the mushroom and wine mixture and continue to stir as it thickens. Stir in the heavy cream and apricot preserves. Let the mixture come to a simmer and thicken, then lower the heat if needed. Stir to dissolve the apricot preserves. Season again with salt and black pepper if needed. Use a small spoon to taste.
Finish cooking the pork chops in the oven until the internal temperature reaches 145 degrees F. Place the cooked pork chops into the mushroom apricot sauce and let them rest for 5 minutes before slicing.
Serve with mashed potatoes and seasonal vegetables.