Place 2 slices of muenster on a slice of bread. Add 3 oz. of ham on top of the cheese. Top with 2 slices of Havarti. Place a slice of bread on top of the Havarti.
Spread 1 Tbsp. of butter on the first side of bread. Sprinkle ¾ oz. of Parmesan on top of the buttered side of bread. Press the cheese into the bread using a spatula. Turn the sandwich over and repeat the process by adding Parmesan to the other side of sandwich.
Store the sandwiches in a covered container between parchment paper layers. Refrigerate until needed, up to 3 days.
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