To a large mixing bowl, add 1 cup of the shredded Swiss cheese, 1/4 cup of the shredded cheddar, the softened cream cheese, ham, mustard, and cayenne pepper (if using). Mix everything together until evenly combined.
1 1/2 cups shredded Swiss cheese, 1/2 cup shredded cheddar cheese, 1 8 oz block cream cheese, 1 1/2 cups diced ham, 2 tsp Dijon mustard, pinch cayenne pepper