Add the Parmesan cheese, Italian seasoned breadcrumbs, Italian seasoning, parsley, garlic, green onions, salt, and black pepper to a medium mixing bowl. Stir until well combined.
Add the ground chicken and gently mix until the seasonings and other ingredients are evenly distributed. Avoid overmixing, as this can make the patties dense.
Divide the mixture into 4 equal portions and shape each portion into a burger patty. Place the patties on a plate and refrigerate for 30 minutes.
Heat a large skillet over medium heat and add the olive oil. Carefully place the chicken patties in the skillet.
Cook the patties for 4–6 minutes per side, or until browned and cooked through.
Top each patty with about 1½ tablespoons of marinara sauce and one slice of mozzarella.
Set the oven broiler to HIGH. Place the burgers under the broiler for 1–2 minutes, watching closely, until the mozzarella is melted and lightly bubbling.
To assemble the Italian Chicken Burgers, spread 1 tablespoon of pesto over the cut side of each top bun.
Add spinach or arugula to the bottom buns, then place a cooked chicken patty on top.
Add a little extra marinara sauce if desired, then finish with the pesto-topped bun. Serve warm.