To a large skillet over medium heat, add oil, swirling the pan to coat. Add the onions. Let them cook for about 5 minutes while you prepare the hamburger patties.
To a large mixing bowl, add ground beef, hamburger seasoning, seasoned salt, and garlic powder. Mix until just combined. Divide the ground beef mixture into four equal portions (4 ounces). Shape each portion into a thin patty, about 5 inches in diameter, or slightly larger than the hamburger buns to allow for shrinkage during cooking.
Arrange the cooked onions into 4 piles. Top each pile of onions with a ground beef patty. Using a spatula, press and flatten the patties into the onions.
Cook the patties for about 4-5 minutes per side, or until desired doneness is reached, carefully flipping the patties with the onions. For medium-done burgers, the internal temperature should be 145°F-150°F. For medium-well, cook to 150°F-165°F.
Just before removing the burgers from the heat, place a slice of cheddar cheese on each patty to melt.
While the burgers are cooking, lightly toast the hamburger buns in a separate pan or in the oven.
Spread a generous amount of fry sauce on the bottom halves of the hamburger buns. Top with 2 cheeseburger patties.
Serve with lettuce, tomato, hamburger pickles, ketchup, and mustard for garnish.