In a large bowl, combine the grated zucchini (with excess moisture squeezed out), grated carrot, ground chicken, garlic, onion powder, garlic powder, oregano, breadcrumbs, egg, Parmesan, parsley, salt, and pepper. Mix until just combined, being careful not to overwork the mixture. Form into evenly sized meatballs.
Preheat oven to 400°F. Heat 1 tablespoon olive oil in a large skillet over medium heat. Add the meatballs and sear until a deep golden crust forms, about 1-2 minutes per side. Add the meatballs to a lined 9x13 baking sheet and bake for 12-15 minutes until cooked through, the internal temperature should be 165F degrees.
Meanwhile, in the same skillet, heat the butter and olive oil over medium heat. Add the onion and cook until softened, about 3–4 minutes. Stir in the garlic and cook for another 30 seconds, until fragrant. Add the orzo and toast for 1–2 minutes, stirring frequently.
Pour in the chicken broth, season with oregano, salt and pepper, and bring to a simmer. Cook, stirring occasionally, until the orzo is tender and most of the liquid is absorbed. Stir in the cream, lemon juice, and zest, and let simmer until creamy.
Nestle the meatballs into the orzo, cover, and cook on low heat for 10 minutes to allow the flavors to come together.
Finish with crumbled feta, extra lemon juice and zest, fresh parsley, and a final pinch of salt and pepper before serving.