Prepare the vegetables by finely chopping the yellow onion, shredding the lettuce, and dicing the tomato and dill pickles. Set the lettuce, tomato, and pickles aside for topping later.
In a small bowl, stir together the ketchup, yellow mustard, and mayonnaise until smooth. This will be the simple burger sauce for the chopped cheeseburgers.
Heat the olive oil in a large skillet over medium-high heat.
Add the finely chopped yellow onion to the skillet and cook for 2 to 3 minutes, stirring occasionally, until the onion softens and starts to turn translucent.
Add the ground beef to the skillet with the onions, breaking it apart with a spatula or wooden spoon into small pieces.
Season the ground beef mixture with the salt, black pepper, and garlic powder, then continue to cook, stirring and chopping the meat as it browns, for about 5 to 7 minutes or until no pink remains.
Once the beef is cooked through, reduce the heat to low and spread the meat mixture evenly across the bottom of the skillet.
Place the cheddar cheese slices evenly over the hot beef in the skillet, allowing them to melt gently for 1 to 2 minutes. You can cover the skillet briefly to help the cheese melt faster.
While the cheese is melting, lightly toast the burger buns in a dry skillet or under the broiler until just golden on the cut sides.
Spread the burger sauce you mixed earlier onto the cut sides of each toasted burger bun.
Spoon a generous portion of the chopped beef and melted cheddar cheese mixture onto the bottom half of each bun.
Top each chopped cheeseburger with shredded lettuce, diced tomato, and diced dill pickles.
Close each burger with the top bun, press gently to help everything settle, and serve the chopped cheeseburgers warm.