Pork Preparation: Combine water, brown sugar and kosher salt for brine. Mix until dissolved. Place pork loin in deep roasting pan. Cover thawed pork loin completely with brine. Refrigerate for 8 to 12 hours to marinate. Preheat oven to 375°F. Remove pork from brine. Rinse well and pat dry. Place pork in oven. Roast for 1 to 1½ hours. Minimum internal temperature should be at least 155°F. Remove from oven. Loosely cover with foil and rest for 30 minutes. Slice the pork loin thin for sandwiches. Refrigerate any additional pork not used for sandwiches.
Mustard Peach Glaze: Combine and mix all ingredients in a mixing bowl.
Caramelized Onions: Peel and julienne onions. Heat olive oil. Blend oil in large sauté pan or skillet on medium heat. Add onions; stirring occasionally, sauté until onions begin to turn golden. Stir in balsamic vinegar, salt and pepper; cook until golden color is achieved.
Sandwich Build: Place 3 to 4 thinly sliced pieces of pork loin and ¼ cup Caramelized Onions in pan and heat through for about 1½ to 2 minutes. Add 1 tablespoon Mustard Peach Glaze to the pork. Allow to caramelize for 1½ to 2 additional minutes. Place 1 slice of Swiss cheese on top on pork mixture to melt. Place pork on heel of toasted roll. Top with crown of roll. Serve immediately.