In a large bowl, combine ground chicken, panko, egg, 3.0 cloves minced garlic, grated onion, 1.0 tbsp lemon zest, dill, oregano, 1.25 tsp salt, 0.5 tsp pepper, red pepper flakes, and 0.25 cup of the feta. Mix gently until just combined.
Scoop and roll into golf-ball-sized meatballs (about 16). Chill in the refrigerator for 10 minutes while you heat the pan.
Heat 2.0 tbsp olive oil in a large deep skillet over medium-high heat. Sear meatballs in batches until browned on 2 sides, about 4 to 5 minutes total. Transfer to a plate (they will finish cooking in the orzo).
Reduce heat to medium. In the same skillet, add 2.0 cloves minced garlic and cook until fragrant, about 30 seconds.
Stir in dry orzo and toast for 1 minute, coating it in the pan drippings.
Pour in chicken broth, 0.5 tsp salt, and 0.25 tsp pepper. Bring to a simmer, scraping up any browned bits.
Nestle the browned meatballs into the orzo. Cover and simmer on medium-low, stirring occasionally to keep the orzo from sticking, until the orzo is al dente and meatballs register 165°F, about 10 to 12 minutes.
Turn off heat. Stir in butter, lemon juice, and 1.0 tsp additional lemon zest until glossy. Fold in spinach to wilt and the parsley.
Sprinkle remaining feta over the top. Cover and rest 2 to 3 minutes to let flavors meld and the orzo thicken slightly.
Drizzle with extra-virgin olive oil if desired. Serve with lemon wedges and additional parsley or feta.
Notes
For lighter meatballs, avoid overmixing the chicken. If the orzo thickens too much as it sits, splash in a bit of warm broth or water to loosen before serving.