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 over medium-high heat. When pan is hot, add the burger patties and season the top generously with salt and pepper. Leave to cook for about 6 mintues and 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 for 5 mintues before serving.
If you want your buns toasted you can brush with butter and place them facedown on skillet, heating just until edges are brown.
Cooking for 6 minutes per side should leave you with patties that are just barely pink in the centre. If you want your burgers well done you can leave them an extra minute or two per side, or cover them for the last 2 minutes.