In a medium bowl, stir together chicken, bread crumbs, garlic, parsley, and parmesan and season with salt and pepper. Form into 4 patties.
In a large skillet over medium-high heat, heat oil. Cook patties until bottoms are golden, 4 to 5 minutes, then flip and add marinara to skillet. Bring to a simmer and top each patty evenly with mozzarella.
Cover and cook until chicken is cooked through and cheese melts.
Spoon sauce from skillet onto bottom halves of burger buns and place patties on top. Top with basil and burger bun tops.