Combine shallots and red pepper. Reserve 2 tablespoons shallot mixture for chutney. Rub both sides of chops with remaining shallot mixture. Place on the unheated rack of a broiler pan. Set aside.
For chutney, combine reserved shallot mixture, brown sugar, vinegar, dried cranberries, and ginger in a medium saucepan. Stir in sweet potato; bring to boiling. Reduce heat and simmer, covered, 10 minutes, stirring occasionally.
Meanwhile, broil chops 3 to 4 inches from heat to desired doneness, turning once (7 to 11 minutes for medium). Serve with chutney. Makes 4 servings.