Use either a 1 1/2" or 1" round cookie cutter to cut 22 rounds from the cheese slices.
Pour a few drops of black food coloring into a small bowl. Dip fine tip paint brush into the food coloring.
Paint seam lines onto each cheese slice creating basketballs.
Potato Rounds
Move an oven rack to the lowest position. Preheat oven to 475 degrees Fahrenheit. Wash potatoes. Cut, using a Mandolin or a knife, into 3/8" thick slices.
Use a 2" round cookie cutter, to cut rounds from each potato slice. Fill a mixing bowl with hot tap water.
Place potato rounds in water and set aside for 10 minutes. Remove potato rounds from water and set on paper towels. Blot dry. Dry out your mixing bowl.
Combine the vegetable oil and 1/2 teaspoon salt in the mixing bowl.
Line a heavy duty baking sheet with non-stick aluminum foil. Pour 3 tablespoons of the oil onto the foil lined pan. Use your hand to swirl the oil around to get an even coating all over the pan. Be sure the get the salt evenly distributed.
Place potatoes in mixing bowl and toss to coat evenly with the remaining tablespoon of oil. Lay potatoes in a single layer on the baking sheet. Sprinkle a pinch of salt over potatoes.
Cover pan tightly with aluminum foil. Bake for 10 minutes. Remove foil and bake for 8 minutes. Rotate pan 180 degrees and continue to bake for 8 minutes. Remove pan and flip potatoes over. Bake for 8-14 more minutes until golden brown.
Remove from oven and place potato rounds on paper towels to remove excess oil. While potatoes are baking, make burgers:
Make Burgers
Tear slice of white bread into small pieces. Place in a mixing bowl. Pour in milk. Use a fork to smash the bread into a paste. Add ketchup, 1/2 teaspoon salt, and pinch of black pepper. Stir to combine.
Add ground chuck and stir just until combined. Scoop out 22 portions of meat by the tablespoonful. Press meat into a 2" round cookie cutter to form into a nice circle.
Heat one teaspoon of vegetable oil on a griddle pan, skillet, or grill pan until smoking. Cook burgers in two batches until well browned on both sides.
If serving these right away, set a piece of cheese on each burger after you flip it to cook the second side and allow the cheese to melt slightly. If you plan to prepare the burgers and potatoes hours before your party, you can reheat them just before serving. Heat your oven to 350 degrees. Place potatoes and burgers on a baking sheet and heat for 5 minutes.
Remove from oven and top burgers with a slice of cheese. Heat just until cheese melts and burger is heated through.
To assemble: set potato rounds on a serving platter and top with lettuce and tomato, if using. Then top with a cheeseburger. Serve immediately.