In a medium bowl, mix together ground turkey, sun-dried tomatoes, parmesan cheese, grated garlic, salt, and pepper using your hands. Form into four equal-sized patties.
Grill turkey burger patties over high-heat until cooked through, about 3-4 minutes per side. During the last minute of cooking, top each burger with one mozzarella slice and heat until slightly melted and bubbly.
Place burgers on split buns and top with pesto and arugula to serve.