Heat a large pan or griddle with the oil to medium heat. Put the tortillas in the pan (in batches if need be) and place a slice of Swiss on each. Spread about 1/2 tablespoon of the mustard over the top of each cheese slice. Stack half of the tortillas with 4 ounces of pulled pork followed by 2 slices of ham. Add 4 pickle slices on top of the ham, then top with a second tortilla (with just the cheese) to make a sandwich. Press the sandwiches lightly and allow the cheese to melt, making sure that the tortillas are nice and crispy.
Slice the sandwiches in half and serve.