Boil the potatoes in enough water until soft, peel the skin and mash it, keep the mashed potatoes aside.
Wash the onion and lettuce very well, peel the onion and slice the onions in slightly thick rings. We only need 4 such rings of onions, as we are preparing four sandwiches, you can save any remaining onion for later use in other recipes. Keep the sliced onion rings aside.
Slice the lettuce leaves in half or you may adjust the size as you need, depending on the size of the bread you are using. Keep this aside. Make sure the leaves are dry.
Heat an iron pan or skillet (or use any non stick pan) and add a tablespoon of butter. Toast the two burger buns on both sides, by flipping once the first side is toasted. Similarly add the remaining 2 tablespoons of butter and toast both sides of the remaining 2 burger buns too. You can also use the burger buns (or sandwich bread) without toasting, but toasting in butter makes them so much more delicious. Keep the toasted buns (or bread slices) aside.
In the same pan or skillet, add the one tablespoon of oil and add the mashed potatoes.
Add salt, garlic powder and black pepper powder, mix well to blend with the mashed potatoes and saute for about 2 minutes. Now the mashed potatoes with garlic and pepper flavor is ready to be used in the sandwich. Keep this prepared mashed potatoes aside.
Take one slice of the bun or bread, add about 1 tablespoon of shredded cheese (slightly adjust the amount of cheese as you would prefer) and microwave for 30 seconds.
Place one layer of mashed potato filling over the melted cheese, top it with sliced onion and lettuce.
Add shredded cheese to the other slice of the bun too and microwave it for 30 seconds so the cheese would melt.
Place the second slice of bun (or bread) on top of the first layer with fillings and gently press. You can gently press the ends of the slice so they would stick together, which will help if you are planning to pack this for traveling.