Brush 1 side of each bread slice with butter. Place 12 bread slices, buttered side down, on ungreased cookie sheet.
Spread each slice with mustard; sprinkle with dill weed. Top with cheese, tomato and remaining bread slices, buttered side up.
Broil 4 to 6 inches from heat for 1 to 3 minutes on each side or until toasted.
To serve, cut each sandwich in half diagonally.