Combine butter, garlic, salt and cayenne in a large bowl and beat at medium speed with a mixer until well combined. Beat in flour. Stir in Emmentaler and ham. Turn dough out onto wax paper and shape into 2 6-inch logs. Wrap in plastic wrap and freeze up to one month.

When ready to bake, allow the logs to thaw on the counter for about 30 minutes. Preheat oven to 350 degrees F. Line a baking sheet with parchment paper. Cut logs into 1/4-inch thick slices. Place slices on baking sheet and bake 10 to 12 minutes or until edges are golden. Transfer biscuits to a wire rack to cool.