How to Make It
Combine 2 cups water, brown sugar, vinegar, 2 tablespoons salt, garlic, peppercorns, thyme, mustard powder and red pepper flakes in a large saucepan and set over high heat. Bring to a simmer and stir until the sugar has dissolved. Remove from the heat and add the ice cubes to bring down the temperature. Once cooled, add the ice cubes to chill then pour into a large re-sealable plastic bag.
Take pork chops and make an incision in each with the tip of a paring knife. Carefully work the tip of the knife into the pork chop to make a small pocket that goes almost to the edges. Add pork chops to brine and place in the fridge for 1 hour.
Preheat oven to 350°F.
Meanwhile, set a large cast iron skillet over high heat. Add a drizzle of olive oil and saute shallot and peppers for 3-4 minutes until translucent. Season with salt and pepper. Set aside to cool. In a large mixing bowl combine shredded provolone, sliced prosciutto and vegetable mix.
Remove the chops from the brine and pat dry with some paper towels (removing the excess moisture on the surface allows the pork chop to sear and caramelize). Stuff each chop with a heaping tablespoon of filling mixture packing it tightly into pocket. Squeeze at ends to seal pork chop. Sprinkle lightly with salt and pepper. Return the large cast-iron skillet over high heat and add a drizzle of oil.Add the pork chops to the pan. Cook over high heat until well browned, about 7-8 minutes. Turn the chops over then place the whole pan in the oven to cook chops through 10-12 minutes. Remove from oven when done and set pan back over medium heat. Remove the pork chops from the skillet and set aside to rest.
For the pan sauce: remove all but 2 tablespoons of fat from the skillet. Add rosemary to pan and cook for 30-40 seconds to infuse the fat. Add wine and deglaze, scraping up any brown bits from the bottom of the pan. Simmer until reduced by half. Stir in the mustard and stock and simmer until slightly thickened, 3-4 minutes. Finish with butter and taste for seasoning. Pour over pork chops when ready to serve.