Heat a large nonstick skillet coated with cooking spray over medium-high heat. Add ham; cook 2 minutes on each side or until lightly browned. Remove from pan; keep warm. Reduce heat to medium; recoat pan with cooking spray. Break eggs into hot pan; cook 1 minute on each side or until desired degree of doneness.
Place muffin halves, cut sides up, on a baking sheet. Spread 2 teaspoons chutney over bottom half of each muffin; top with 2 ham slices, 1 egg, and 1 tablespoon cheese. Sprinkle 2 tablespoons cheese over top half of each muffin. Broil 1 1/2 minutes or until bubbly. Place top halves of muffins over the bottom halves.