Add the parmesan cheese, bread crumbs, Italian seasoning, parsley, garlic, green onion, salt, and pepper to a medium mixing bowl. Mix to combine.
Add the ground chicken to the mixing bowl and gently mix until everything is evenly distributed.
Form the chicken mixture into 4 patties and place on a plate. Refrigerate the patties for 30 minutes to allow the flavors to marry together.
Place a large skillet (see note) over medium heat and add the olive oil to the pan. Add the patties to the skillet and cook for 4-6 minutes per side until cooked through and browned.
Top each burger with 1 1/2 tablespoons of marinara and a slice of mozzarella cheese.
Set your oven's broiler to HIGH and put the burgers under the broiler to cook for 1-2 minutes until the cheese has melted. Carefully remove the burger from the oven.
To assemble: Spread 1 tablespoon of pesto on the cut side of the top bun. Add some spinach and/or arugula to the bottom bun. Place the burger patty over the greens and spread a little more marinara on the patty, if desired. Place the top bun over the patty and serve warm.
Notes
If you have an oven-safe skillet, I recommend using it to cook the burgers so it can go right under the broiler. If you don't have one, that's okay too. You'll transfer the burgers to a baking sheet once they're cooked and then top the burgers with sauce and cheese before broiling.