1. Stir together 1/2 cup mayonnaise and next 6 ingredients; gently stir in cheese. Cover and chill up to 3 days, if desired.
2. Spread remaining 1/4 cup mayonnaise evenly on 1 side of each bread slice. Place 4 bread slices, mayonnaise sides down, on wax paper.
3. Spread cheese mixture evenly on top of 4 bread slices on wax paper; top with remaining bread slices, mayonnaise sides up.
4. Cook sandwiches, in batches, on a hot griddle or in a large nonstick skillet over medium heat 3 minutes on each side or until golden brown and cheese melts.
Note: For testing purposes only, we used Sara Lee Whole Grain White Bread.