Line a small baking sheet or plate with parchment paper. Portion the nacho cheese dip into 6 equal portions using a small ice cream scoop and place onto the prepared baking sheet. Freeze for at least 4 hours, or you can do this step the day before and freeze overnight.
When ready to make the burgers, preheat a grill or grill pan to medium high.
Add the beef into a large bowl and sprinkle on the chiles, sambal, 2 teaspoons salt and a few hefty grinds of black pepper. Gently mix with your less dominate hand until just combined. Divide the mixture into 6 equal portions. Take 1 portion and flatten slightly. Add 1 portion of the frozen nacho cheese to the center of the patty and wrap the edges up and around, pinching to cover. Repeat with the remaining portions.
Add the burgers to the grill over direct heat and cook until the burgers easily release from the grill, about 4 minutes. Then, gently flip and cook the burgers on the other side just 2 minutes more. Transfer the burgers to a serving platter and allow to cool slightly while grilling the buns.
Brush the cut side of each bun with some of the melted butter. Grill the buns buttered-side down until golden and toasted.
Sprinkle the avocado slices with the lime juice and a sprinkle of salt. In a large bowl, whisk together the hot sauce with the confectioners' sugar until dissolved, then add the lettuce and toss to coat.
Build the burgers by starting with a bottom bun, then add a slice of pepper Jack cheese, a burger, avocado slices, a mound of dressed lettuce and a top bun. Repeat with the remaining ingredients.
You can always divide the beef into 12 even mounds and flatten them. Then for each burger, sandwich a portion of the nacho cheese between 2 mounds of beef and pinch the edges. Or, if you have a burger-stuffing gadget, use that on the setting to make the thinnest patty possible.