3 to 4 tablespoons butter, melted
8 slices whole wheat bread, not too thick
4 3/4-ounce slices processed American cheese
8 vertical slices of dill pickle
8 thin slices ripe medium-sized tomato
12 to 16 red onion rings
4 1 1/2-ounce slices Sharp (aged) Wisconsin Cheddar
Using a pastry brush, butter each slice of bread on one side, and place 4 slices, buttered side down, on a work surface. Place on each of these slices one slice processed American cheese, 2 slices dill pickles, 2 slices tomato, 3 to 4 red onion rings and 1 slice of Cheddar. Top with the remaining 4 bread slices, buttered side up.
Lightly butter and heat a griddle or heavy skillet until hot. Place 2 sandwiches in the skillet and weight with another heavy pan or skillet. Brown slowly on one side for 2-3 minutes before turning, with a spatula, and grilling the other side until brown and cheese melts. It may be necessary to add a bit of butter to the skillet.
Repeat with remaining two sandwiches. Serve immediately.
If you like, you may spread mayonnaise or mustard on the unbuttered sides of the bread.