Preheat panini press (alternatively, you can use a grill pan or skillet if you don't have one).
Spread 1/2 tablespoon of butter on each slice of bread. Flip bread over.
In a small bowl, mix mayonnaise (2 tablespoons) and dijon mustard (2 tablespoons) together. On the non-buttered side of the bread, spread 1/2 tablespoon of mixture on each slice.
On four slices of bread, stack the ham, apple slices, and swiss cheese evenly in that order. Flip the remaining slices of bread butter side up on top to complete the four sandwiches.
Add the sandwiches one or two at a time (depending on how big your panini press is) to the press, pressing down firmly for 5 seconds and leaving it to cook for approximately 3 minutes, or until golden brown on the outside and the cheese is melted on the inside.
Serve hot off the press!
The provided nutrition information does not include any added sodium from seasoning to taste, any optional ingredients, and it does not take brands into account. Feel free to calculate it yourself using this calculator or by adding the recipe to Yummly.