Divide 1 ounce smoked gouda between 1 top and 1 bottom of a croissant. Sprinkle each half with 1 tsp Parmesan. Top each with about 3 slices of salami, top half of the sandwich with a small handful of arugula.
Close the sandwich and continue with the remaining sandwiches. Grill the panini until the cheese melts, about 3 to 4 minutes.