Combine the brine ingredients in a dutch oven large enough to hold the brine and eventually the chops. Bring to a boil and stir to dissolve salt. Let the brine cool before adding the chops. Cover and refrigerate overnight.

When ready to cook drain the brine off the chops and pat them dry with a paper towel.

Preheat oven to 350 degrees.

Sprinkle the chops with black pepper. Heat 2 Tbsps oil in an ovenproof skillet over medium high heat. Add pork in single layer and brown about 3 minutes on each side.

Add 1 tablespoon butter and sage to the skillet. Baste the chops with the butter. Transfer the skillet to the oven and bake until internal temperature is 145 degrees F. This may take 30 minutes or so if you chops are thick. Remove pork from oven, cover them loosely and allow them to rest about 3 minutes.

In a small saucepan, cook the sugar over medium heat until melted and deep golden brown, about 5 minutes. Mixture will be thick. Be careful not to burn. Add the vinegar and stir until hardened sugar dissolves. Add the broth and sage. Boil until mixture is reduced to ⅓ cup. This may take 10-20 minutes depending on the size of your sauce pan. You can make the sauce a day ahead, chill and reheat just before serving.

Transfer chops and pan juices to a serving platter. Drizzle the sauce over the chops and serve.