Stir together 1 cup mayonnaise, diced pimiento, Worcestershire sauce, and onion. Stir in shredded sharp Cheddar cheese.
Spread 1/4 cup
pimiento cheese mixture on 1 side of a bread slice; top with
another bread slice. Lightly spread both sides of sandwich with
mayonnaise. Repeat with remaining pimiento cheese mixture for desired
number of sandwiches.
Cook, in batches, on a hot griddle or large
nonstick skillet over medium heat 4 to 5 minutes on each side or until
golden brown and cheese melts.