For the brine and pork chops: 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 and the ice cubes have dissolved, add to a resealable plastic container (or a plastic bag) and add the pork chops. Place in the fridge for 1 hour.
Tie each pork chop around the perimeter with a piece of kitchen twine. This will help the chop retain a nice, round shape while cooking.
Preheat the oven to 350 degrees F.
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). Sprinkle lightly with salt and pepper. Set a large cast-iron skillet over high heat. Coat the pan with oil and when the oil starts to smoke, add the pork chops to the pan. Cook over high heat until well browned, 8 to 10 minutes. Turn the chops over and reduce the heat slightly to allow the chops to cook through. Cook on the second side until golden brown, about 8 minutes. When done, remove the pork chops from the skillet and place onto a sheet tray. Divide the slices of the Brie between the chops and layer evenly on each so they are covered well. Place the sheet tray into the oven and cook until the Brie is just melted and the pork has cooked to 140 to 145 degrees F. Remove from the oven and transfer the chops to a plate to rest.
For the pan sauce: Meanwhile, place the skillet back over medium-high heat. Add a drizzle of olive oil and then add the apples and onions. Saute for 4 to 5 minutes, and then add the Calvados. Allow the alcohol to cook off (you can flambe at this stage if desired by igniting the Calvados in the pan). Once the Calvados has reduced, add the stock and simmer. Season with some salt and pepper. Allow to reduce for 2 to 3 minutes, and then remove from the heat and swirl in the cold butter cubes. This will thicken the sauce and give it a nice sheen. Serve the Brie-topped pork chops with the sauce.