Mix ground chicken, panko, egg, half the garlic, 1/4 cup Parmesan, Italian seasoning, 1/4 teaspoon salt, and 1/8 teaspoon pepper. Shape into 16 small meatballs.
Heat a large skillet over medium heat. Cook the meatballs in a thin film of oil, turning often, until browned and cooked through, 10 to 12 minutes. Transfer to a plate.
Cook spaghetti in salted water until just al dente. Reserve 1 cup pasta water, then drain.
Melt butter in the skillet. Add remaining garlic and cook for 30 seconds. Stir in broth and scrape up browned bits.
Add spaghetti and 1/2 cup reserved pasta water. Toss until glossy, adding more water as needed. Season with remaining salt and pepper.
Return meatballs to the skillet. Finish with remaining Parmesan and parsley, then serve hot.