Combine arugula, parmesan and garlic together in a food processor. Process until arugula is chopped fine. With food processor running slowly drizzle in olive oil until mixture emulsifies. Season to taste with salt.

To make a sandwich, spread butter on one side of each slice of bread. Spread a thin layer of pesto on the non-buttered side. Place 1/4 cup of cheese on top of the pesto, top with two slices of ham and 1/4 cup more cheese top with the other slice of bread, pesto side down. Repeat with remaining ingredients until 4 sandwiches are made.

Heat a skillet over medium heat. Cook sandwiches until bread is golden and cheese has melted, 2 - 3 minutes per side. Serve.