In a large bowl, gently combine the beef, marjoram, basil, oregano, salt, pepper, chopped black olives, sun-dried tomatoes and Parmesan. Divide into two equal portions and shape into patties. Cover and refrigerate for 30 minutes.

Preheat a clean grill to medium-high heat. Brush the patties lightly with the melted butter. Grill, turning carefully, until the center of each patty reaches 160°F (71°C) on a food thermometer. Start checking around 5 minutes per side; thickness and grill heat determine the cooking time.

Lightly toast the cut sides of the focaccia on the grill. Spread the bottom halves with basil mayonnaise, add arugula, then the cooked burgers and mozzarella. Spread the top halves with basil mayonnaise and close the burgers. If you use toothpicks to hold them together, remove them before eating.

While the patties chill, combine the mayonnaise and fresh basil in a small bowl. Refrigerate until ready to assemble the burgers.

Cut the focaccia into squares large enough for the burgers and then slice in half to create a top and bottom.