In a small bowl, combine all the ingredients for the special sauce. Cover and refrigerate until ready to use.
Preheat a lightly oiled grill or grill pan over medium-high heat.
Butterfly the hot dogs! Slice each hot dog lengthwise almost all the way through—you want the dog to remain attached on one side—then fold it open like a book.
Grill the dogs for about 4 to 5 minutes per side or until lightly charred. During the last 2 minutes of cook time, arrange the dogs into 4 pairs of side-by-side dogs. (These are your “patties.”) Top each pair with a slice of cheese and allow it to melt.
If you like grilled buns (who doesn’t?), place the buns on the grill cut side down on the grill for about 30 seconds to 1 minute, just until grill marks appear.
Add a burger dog to the bottom of each bun and top with tomato, lettuce, and plenty of special sauce. Sandwich everything together and go to town.