Caramelize Onions - Melt butter over medium-high in a large cast-iron skillet. Add onion and sprinkle onions with sugar, salt, and pepper. Cook for 20 minutes to carmelize. Add 2 tbsp of water every 5 minutes and stir often to prevent sticking. When soft and golden brown, transfer onions to a bowl, and wipe out the skillet with a paper towel.
Form Patties - Divide meat into equal portions. Roll each portion in to a ball and press each down with your hands until they are ¼-inch thick and 4-inches wide. Season both sides of the patties with salt and pepper.
Form Burgers - Add 1 slice of cheese to the center of a patty. Fold any overhanging cheese back in. Top cheese with another patty, seal the edges tightly with your fingers. Round the edges a little. Repeat to form additional burgers.
Cook Burgers - Add the oil to the skillet to lightly coat the bottom. Heat skillet over medium-high until scalding hot, about 2 minutes. Add the burgers and cook 5 minutes on one side, then flip and cook about 2-3 minutes more. Transfer burgers to a paper towel-lined surface to rest.
Toast Buns - Scrape up any cheese that might have escaped into the pan. Reduce heat to medium, place bun halves cut-side down and toast for about 1 minute. Lay pickles on the bottom halves, and then add burgers, caramelized onions, and finish with the bun's top. Serve immediately.