Melt butter in the skillet over medium high heat. Add onion with a pinch of sugar and salt.Saute stirring few times, over medium heat for 30 minutes. Remove from the heat and let it cool.
In a mixing bowl, combine and whisk together mayo, ketchup, finely chopped chives, finely diced dill pickles, caramelized onions and a pinch of salt.Mix together. The sauce is ready.
Burger
Cook sliced onions over medium-high heat with 1 tablespoon of butter until seared golden color, on both sides.
In a seasoned cast iron skillet over medium-high heat. Add 2 beef balls and press down using a spatula. Season with salt over the top.Sear the burgers for 2-3 minutes on both sides.
Melt two slices of cheddar cheese to both patties. Repeat with the rest of the beef balls.Place seared onion on the first patty, top the onion with the second patty.