Grill the hot dogs until nice and charred on both sides, 3 to 4 minutes per side. Butter the cut sides of the hoagie roll halves and grill, cut side-down, until charred, 1 to 2 minutes.
Using a skewer or the tip of a small paring knife, poke about 10 holes in the bottom of a TK pan. Spray the entire pan with nonstick cooking spray (this is an important step). Now, layer in this order: one-third each of the charred hot dogs, Cheddar, provolone and salami. Repeat the layers 2 more times, making sure to finish with a layer of salami. Make sure that every layer is a snug fit, like you would a lasagna.
Put the pan on the grill and close the lid. Grill until the cheese has melted, 8 to 10 minutes. Remove from the grill and let rest for about 5 minutes. Run a paring knife around the edge of the pan to loosen the loaf. Turn the pan out onto a cutting board, unveiling the hot dog loaf. Slice the loaf crosswise into 6 pieces, just as you would a meatloaf. To build your sandwich: start with your hot dog loaf on the bottom bun, then top with mustard, lettuce, tomato and a sprinkling of celery salt. Finish with the top bun.