In a skillet, melt the butter over medium heat. Add the onions and cook, stirring occasionally, until they are caramelized and golden brown. This should take about 15-20 minutes.

While the onions are cooking, season the ground beef with salt and pepper. Form the beef into two equal-sized patties.

Heat another skillet or grill over medium-high heat. Cook the patties to your desired level of doneness, usually about 4-5 minutes per side for medium.

Place a slice of cheese on each patty during the last minute of cooking, allowing it to melt.

Once the onions are caramelized, place them on top of one of the patties, then add the other patty on top, cheese side down, to create a double-layered burger.

Toast the bread or buns in the skillet until lightly browned, then place the burger between the slices or in the bun.