In a 12-inch skillet, melt the butter over medium heat. Add the apple slices and thyme. Cook, stirring occasionally, until the apples are slightly soft, about 4 minutes. Cool for 5 minutes.
Preheat a panini press. Spread each bread slice with 1 tablespoon mustard. Arrange 1/4 cup of cheese on each of 4 bread slices and top with 2 slices of ham. Divide the apple mixture evenly on top of the ham. Add the remaining cheese and cover with the remaining 4 bread slices. Grill in the panini press until the cheese has melted and the tops are golden and crispy, about 5 to 6 minutes.