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MELT butter in medium nonstick skillet. Add onion. Cook over medium-high heat until tender, stirring often. Reduce heat to medium-low. Stir in sugar; cook 15 to 20 minutes until onion is glazed and caramelized. Stir in mustard.
TO prepare each sandwich: place 2 slices cheese and 3 slices ham on bottom slice of bread. Spoon 1/4 cup onion mixture over ham. Top with 2 more slices cheese and cover with top slice of bread. Repeat with remaining ingredients.
COAT an electric grill pan with nonstick cooking spray. Grill sandwiches about 5 minutes until golden and cheese melts.