Preheat oven to 450°F. Arrange the bread slices on a baking sheet lined with baking paper, then spread half of the butter (2 tablespoons) evenly on one side of the bread. Toast for 3 to 4 minutes, or until golden brown.
Remove from the oven, flip the bread over, and spread the remaining 2 tablespoons of butter on the untoasted side. Toast for another 3 to 4 minutes.
Spread a thin layer of Dijon mustard on each bread slice. Top with the shredded Gouda and Havarti, 2 slices of ham, and a few apple slices. Sprinkle a little more cheese to help hold everything together.
Return the baking sheet to the oven for another 6 to 7 minutes, or until the cheese is melted and the bread is toasted and golden brown.
Remove from the oven. Grind black pepper over each piece of toast. Top with a handful of arugula, then finish with a generous drizzle of hot honey. Serve hot.