Layer each sandwich with romaine lettuce, tomato slices, ham, and Swiss cheese.
Top with the remaining slices of bread and cut in half.
In a blender, combine the banana, maple syrup, vanilla extract, milk, water, and ice cubes. Blend until smooth. Adjust sweetness or consistency by adding more milk or ice if needed.
Serve the ham and Swiss sandwich with chips, pickles, and Korean banana milk.