You'll need a sharp knife, a sturdy metal burger turner and 2 large, heavy skillets (well-seasoned cast iron works very well; Teflon will not work.)
Preheat the first skillet over medium-high heat. The second skillet should be preheated to be slightly less hot. Smear the inside of the second skillet with a thin coat of butter. When the first skillet is hot enough to instantly sizzle a small test piece of burger, place the 4 patties inside. Set the buns, crust side up, in the second skillet. Wait 30 seconds or so, then turn the patties and press them down so they spread a bit and stick to the skillet surface. Wait 2 minutes, then remove the lower halves of the buns and coat the toasted surface with mayonnaise. Add 2 slices of tomato and then cover tomato with sliced lettuce. Set aside. When the patties are almost done to your taste, turn them a second time, let them cook a few more seconds until you think they're just right, then remove from the pan.
You're through cooking. Next step is to assemble the whole thing. Place 1 beef patty on top the dressed lower half of the hamburger bun. Then stack in this order: 1 slice of ham, 1 slice of cheese, a second slice of ham, a second beef patty, and finally the top half of the hamburger bun.
In a few seconds, the heat from the hamburger patties should melt the cheese and weld the entire assembly into 1/2 pound of heaven on a bun.
Serving suggestion: French fried potatoes.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.