Another easy one, based on a sandwich from New Orleans.
Small round hard-crusted rolls (about 3-inches in diameter), sliced in two halves for sandwiches
-- These are intended to resemble ten-inch round Italian bread, which is usd for the authentic full-sized sandwiches
Prepared olive salad marinated in olive oil, minced if it doesn't already come that way
Lots of minced garlic mixed with the olive salad (if it doesn't already have some)
I'm sorry I don't have exact amounts -- I just kind of estimate, depending on how many I want to make. I would use a double-thickness of ham and cheese, as the sandwiches are fairly tall and stuffed.
Layer the meats and cheese on the rolls, and top the meat/cheese with a generous amount of olive salad.
If the olive salad is light on the olive oil, you can spread a bit of olive oil directly on the bread slices. I usually at least put some olive oil on the bottom bread slice which isn't next to the olive salad.
Secure sandwiches with toothpicks.
Put into a warm oven until the sandwiches are warm and toasty, and the cheese is melty but not running off the bread.
Serve warm (but can be eaten cold).
If you want to make your own olive salad, the typical stuff from New Orleans includes green olives, pimientoes (but not too much of these), cauliflower, celery, carrots, capers, oregano, and lots of garlic, all of which are marinated in olive oil. (You can buy the cauliflower pre-marinated.) The salad also usually contains peperoncinis -- I think that's the same pepper that Olive Garden puts in their salads. There are some good recipe online.
Different recipes add different things to the olive salad, such as green onions, parsley, or other kinds of sweet peppers (not jalopenos!) Some recipes include black olives, but in my experience, a "real" New Orleans muffaletta has green olives only.
For a ten-inch muffaletta, the veggies would be cut in chunks (a bit larger than diced). For the mini-muffalettas, you'd want to mince the veggies, so they don't fall off the bread.
You can also use the olive salad, spread on French bread, as bruschetta.
If you want "authentic New Orleans," then the muffaletta actually contains capicola ham and genoa salami, but that can get pretty expensive. I find the more generic (and cheaper) versions work just as well for the mini's. An authentic regular-sized muffaletta would also probably contain mozzarella, but for the mini's you don't want too many layers or the top slice of bread will fall off.
Last of all (contrary to what is served in many restaurants outside New Orleans) an authentic muffaletta does not contain mayonnaise, mustard, butter, lettuce, tomatoes, jalopenos, or turkey!