In a large bowl, combine the ground chicken, panko breadcrumbs, grated parmesan, egg, minced garlic, shallot, oregano, salt, and black pepper. Use a light hand and mix just until everything is evenly incorporated; overmixing can make the burgers dense.
Divide the mixture into 4 equal portions and gently form into patties about 3/4 inch thick. If the mixture feels loose, let it rest for 5–10 minutes to help the breadcrumbs hydrate and the patties firm up.
Preheat a skillet over medium heat and add olive oil. Once shimmering, add the patties and cook about 4–5 minutes per side, until a nice crust forms and the internal temperature reaches 165°F (74°C).
In the last 2 minutes of cooking, spoon a small amount of marinara onto each patty and top with a slice of mozzarella. Cover briefly to melt the cheese, about 1–2 minutes. If you prefer more sauce, you can add another tiny dollop after melting the cheese.
Toast the buns in the remaining pan oil for 1–2 minutes until lightly golden. If you like a glossy bun, brush the cut sides with a bit of marinara or olive oil.
Assemble the burgers: spread a thin layer of marinara on the bottom bun, place the cheesy chicken patty, add a bit more marinara if desired, top with arugula or lettuce, and finish with the top bun. For extra brightness, sprinkle chopped basil on top.
If you prefer a bigger flavor punch, you can brush the inside of the buns with a touch of garlic butter before toasting, or add a whisper of red pepper flakes to the patties before forming.
Serve immediately with a side of salad, roast vegetables, or crispy oven fries. Leftovers keep well in the fridge for up to 3 days; reheat gently to keep the patties juicy.