In a large pot, bring 7 cups water to a boil. Remove from heat and add 1/2 cup salt, the brown sugar, rosemary sprig, and 2 tsp. peppercorns, stirring until salt and sugar are dissolved. Add ice cubes and chill until cold. Place pork in brine and set a plate on top to keep meat completely submerged. Cover with plastic wrap and chill overnight.
Heat 2 tbsp. oil in a large frying pan over medium heat. Add onions and cook, stirring often, until transparent and starting to brown, 10 to 15 minutes. Turn heat to low; add peaches, granulated sugar, vinegar, and remaining 1 tsp. peppercorns. Cook, stirring often, until marmalade is caramelized and sticky, 40 minutes. Stir in remaining 1 tsp. salt and 2 tsp. rosemary.
Prepare a charcoal or gas grill for medium heat (350° to 400°; you can hold your hand 5 in. above cooking grate for only 5 to 7 seconds). Remove pork from brine and pat dry. Brush pork all over with remaining 1 tbsp. oil.
Grill pork, covered, turning once, until meat is done the way you like it, about 10 minutes for medium-rare (145°; cut to test). Transfer pork to a platter, tent with foil, and let rest 5 to 10 minutes. Serve with marmalade.
Note: Nutritional analysis is per serving.
*Sodium content could not be accurately calculated.