Assemble the sandwich by buttering the one side of each slice with about a half tablespoon total of butter then stacking the cheese slices and arugula and patting down to close.

Melt the remaining butter in a nonstick skillet over medium-high heat. Place the sandwich in the frying pan and press down with a spatula. Cover, lower heat and cook on one side. When browned, flip and cook on remaining side, adding an additional dab of butter if necessary. When browned, crisp and golden, remove, cut in half diagonally and drizzle with Greek honey.

Serve!