Heat the oil in a large skillet over medium heat. Add the chopped onion and cook until it starts to soften, then add the grated carrot. Cook until the vegetables are tender and lightly sweet.
Transfer about half of the sautéed onion and carrot to a large bowl. Leave the remaining half in the skillet for the sauce.
Add the ground chicken, cooked rice, salt, black pepper, Italian seasoning, and garlic powder to the bowl with the sautéed vegetables. Mix gently just until combined.
Lightly wet your hands with water, then shape the chicken mixture into meatballs. The mixture will feel soft, but the cooked rice helps it hold together.
Add the butter to the skillet with the remaining onion and carrot. Once melted, sprinkle in the flour and stir for about 1 minute.
Slowly pour in the water while stirring, then add the heavy cream. Season with salt, black pepper, and Italian seasoning. Stir until the sauce looks smooth and creamy.
Nestle the chicken meatballs into the white sauce. Cover the skillet and cook for 10 minutes.
Gently turn the meatballs, cover again, and cook for another 10 minutes, or until the meatballs are cooked through and tender.
Spoon the white sauce over the meatballs and serve warm.