For the donkey sauce: Combine the mayonnaise, roasted garlic puree, mustard, salt, pepper and Worcestershire sauce in a medium bowl. Refrigerate for 30 minutes before using.
For the SMC: In a 2-quart saucepan, bring the half-and-half and water to a simmer over medium heat. Maintain medium heat and add the hot sauce and Worcestershire sauce. Using a whisk, mix in the processed cheese 2 ounces at a time until it has fully incorporated.
Using the same method of adding the cheese slowly, add in the other cheeses. Continually mix until all the cheese has melted and the sauce is smooth. Once you start mixing in the cheese you must whisk constantly until the cheeses are fully incorporated. Once fully incorporated remove the sauce from the hot saucepan.
For the real deal with cheese: Form 4 round burger balls. Sprinkle with salt all over. On a hot griddle, place the burger balls and allow to sear for 45 seconds. Using burger spatulas, smash the burgers to a 1/4-inch thickness. Once the juice comes to the surface, about 1 minute, flip the burgers to a new spot on the griddle.
Top each burger with 1 tablespoon of SMC. Cover with 1 slice of Cheddar. Place a dome over the burgers and add water underneath (use a squeeze bottle) to steam and melt the cheese. After about 1 minute remove the dome and remove the burgers from the heat.
Spread the melted garlic butter on the cut sides of the buns. Toast both sides of the bun halves until golden brown.
To assemble: Spread donkey sauce on the cut sides of the buns, edge to edge (about 6 tablespoons total). On the bottom half of the buns stack in the following order: pickles, onions, burger, then top with tomato, lettuce and place top bun on top. Secure with 6-inch bamboo skewers.
Start with blocks of cheese and shred by hand for best results.