Combine meat, mayo and fish sauce in a large bowl. Form into 4 patties and make a small depression with your thumb in the center of each patty. Sprinkle with freshly ground pepper on both sides.
Heat a grill or flat top griddle to 375 degrees. Cook according to your preferences, trying to minimize the amount of flips. It will take 6-8 minutes per side for a medium-well burger. Do not press down on the burgers during cooking. Top with American cheese during the last minute of cooking.
During the last minute of cooking, brush tops of burger buns with melted butter. Grill directly on the grill grates until slightly toasted.
For the special sauce, combine all ingredients in a small bowl. Set aside.
Assemble the burgers: Place the burger onto the bottom half of the bun. Top with special sauce, slice of tomato, some lettuce and potato chips. Top with toasted bun.