On 2 slices of bread, layer white American cheese, shaved deli ham, cheddar cheese slices & another slice of bread. Spread each top slice of bread with 1/2 tbsp butter then place sandwich buttered side down on griddle or in skillet over medium heat. Spread top slice of each sandwich with 1/2 tbsp butter. Cook 2 to 3 minutes each side to make golden & the cheese begins to melt. Set aside.
Spread one side of remaining 2 slices bread with 1/2 tbsp each of the remaining butter. Cook buttered side down on griddle or skillet to toast.
Place grilled ham & cheese sandwiches on a plate or cutting board. Spread top side of each with 1 tbsp mayo. Top each with tomato slices, a sprinkle of pepper, 4 of the half slices of crisp bacon, & lettuce. Spread the un-toasted side of the two single toasted slices of bread with 1 tbsp mayo each. Place mayo side down on top of sandwiches.
Cut each sandwich into quarters. Top each quarter with a bread & butter pickle slice & skewer through the pickle & sandwich with a toothpick. Stand sandwich quarters crust side down & points up around plates & place chips, if desired, in the center.