The Mozz Makes the Hero at Dave and Tony's Salumeria
I wouldn't call Dave and Tony's Salumeria in Astoria a "secret" sandwich shop, but they don't shout their heros from the rooftops either. Ask for one and they'll direct you to a shelf of fresh bread from Astoria Bakery and ask what you want on it.
I'd recommend the mozzarella, which is made in-store. Though not incredibly tender or flavorful, it's quite fresh, clean and milky with a slight chewiness. The mildness goes well with some thinly sliced prosciutto di Parma, hot sopressata, and spicy peppers (request a generous amount of those) for a sandwich that balances salt and fat with some pickled heat. Prices vary by bread and filling; this combination will run you $9.
As for your bread options, ask if they have the sesame seed-topped semolina heros in stock—the same excellent ones you'll find at Rosario's. The bread in the photo above makes a good sandwich, a little dense with a crackly crust, but Astoria Bakery's crustier, pointy-ended rolls may be even better.