Press each ball flat, to about ¼ of an inch thick.
Fold each slice of cheese into fourths, you will end up with a little square.
Place the squares of folded cheese onto 4 of the patties, then cover with the remaining 4 patties. Gently press the edges of the burger to seal the top and bottom layer, then gently form into rounds with your hands.
Place a heavy non-stick skillet or cast iron pan over medium high heat. When the pan is hot place the patties in the pan and season the tops generously with salt and pepper. Leave the patties to cook for about 6 minutes, then flip.
After you flip your patties, season again with salt and pepper. Cook for another 6 minutes.
Remove from the heat and transfer to a plate. Allow the burgers to rest 5 minutes before serving.
If you want your buns toasted, you can brush with butter and place them face down on a skillet, heating until edges are golden and crispy.