Lay the eggplant slices on a baking sheet in a single layer and brush liberally with the Homemade Italian Dressing. Roast in the oven until cooked through and golden, 12 to 15 minutes.
Build the sandwich on the rolls with the mozzarella first, then the salami, capicola, prosciutto, mortadella, roasted eggplant and top with the lettuce, tomato and a generous drizzle of the Homemade Italian Dressing. Serve while blasting Louis Prima.
Homemade Italian Dressing:
Place the vinegar, mustard, sugar, Italian seasoning, salt, pepper, garlic and shallots in a blender or food processor. While the machine is running, slowly drizzle the olive oil through the blender top or feed tube until the dressing is combined and emulsified. Adjust the seasoning if necessary; add more oil if you want it less acidic. Store the dressing up to 2 weeks in the fridge.