Position an oven rack in the top third of the oven and preheat the oven broiler.
Remove the stems from the mushrooms and discard. Lay the mushroom caps gill-side-up and use a sharp knife to completely remove the gills (so that the caps will lie flat). Arrange the mushroom caps on a baking sheet, brush all over with 1 tablespoon of oil and sprinkle with 1/4 teaspoon salt. Broil until the caps are just tender, flipping halfway through, 4 to 5 minutes per side. Allow to cool completely.
Whisk together the vinegar, pepperoncini, oregano, remaining 1 tablespoon oil and a few grinds of black pepper in a small bowl.
Assemble the sandwiches: Arrange one mushroom cap, cut side-up, on a work surface. Fold 1 piece of provolone to fit on top of the cap and repeat with 1 slice each of ham and salami. Top with 1 slice of tomato and about 2 tablespoons of lettuce. Drizzle with some of the pepperoncini vinaigrette. Sandwich with another mushroom cap and secure with a toothpick threaded with an olive. Repeat with the remaining ingredients to make 3 more sandwiches. Wrap each sandwich halfway in wax paper (this will help catch all the juices) and serve.
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From Food Network Kitchen