Bring a pot of water large to boil (large enough to submerge your head of cabbage).
Once boiling, add cored cabbage and blanch for about 3 minutes, then use 2 tongs to remove each of the leaves. If they're difficult to remove, allow the leaves to blanch longer. Set blanched leaves aside on a plate as you cook remaining leaves. You'll need 8 leaves in total, so feel free to discard the center smaller leaves. Place leaves on kitchen towels or paper towels -- you want to remove as much liquid as possible here to prevent your wraps from becoming soggy!
Once leaves are cool enough to handle, use a small knife to remove some of the core's thickness by dragging the blade over the top of the core.
Working one cabbage leaf at a time with the stem facing toward you. Start with a layer of mayo and mustard, followed by 1 slice of cheese, 2 slices of ham, and 3 pickles.
Fold the wraps like a burrito -- fold the left and right sides over the filling, then tightly roll the wraps away from you.
Optional: Preheat oven to 400 F and bake the cubanos for an additional 15 minutes to get the cheese melty!
Slice in half, and enjoy!