Lay out 7"x5" slices of ham. Cover each with a slice of prosciutto and a slice of Gruyre, and top with a second slice of boiled ham. Cut each into 6 squares.
Beat the oil, eggs, pepper to taste, and the cayenne together in a shallow bowl. In another bowl toss sesame seeds, bread crumbs and chopped parsley together.
Preheat over to 400 F.
Dip each square first into flour, next into the egg mixture, last into sesame seed mixture.
Put squares on a buttered baking sheet and drizzle melted butter on top. Bake for 10 to 13 minutes, until sandwiches are golden and cheese is melted. Drain on a paper towel for 1 minute. Serve immediately.