Begin by preparing the brine. In a medium bowl, whisk together the water, salt, and 1 teaspoon of the fresh rosemary until the salt has dissolved.
Place a gallon-sized ziplock bag in a large bowl. Place the pork chops in the bag, and fill the bag with the brine. Seal it and place the bowl with the bag in the refrigerator. Allow the pork chops to brine overnight.
Preheat the oven to 400 degrees Fahrenheit with 2 cast iron skillets inside of it.
Remove the pork chops from the brine, rinse them, and pat them dry. Rub them with the olive oil, and season with the remaining 2 teaspoons rosemary and the black pepper.
Use oven mitts to transfer the to skillets to the stovetop over medium high heat. Sear the pork chops until golden, fitting 2 per pan, about 5 to 7 minutes. Flip them and immediately transfer to pans to the oven.
Roast until the thickest part of the pork chops reach 145 degrees Fahrenheit. Serve with the cranberry glaze, which you can prepare while they finish in the oven.
Bring the water and brown sugar to a boil over medium-high heat. Add the cranberries, lower the heat to medium, and cook until the cranberries soften, about 5 to 8 minutes. Add the balsamic, rosemary, salt, and nutmeg and stir to combine.
Cook until the glaze has thickened but the cranberries are still visible and not complete pulp, about 5 minutes more, stirring once or twice. Remove from heat and set aside.