Prep the Oven: Preheat your oven to 350°F (175°C). Line a large, rimmed baking sheet with parchment paper to ensure the rice balls don't stick.
Mash the Veggies: Place your steamed carrots and broccoli in a large mixing bowl. Use a fork or potato masher to crush them until only very small, manageable chunks remain.
Create the Flavor Base: Add the lightly beaten egg, shredded white cheddar, garlic powder, salt, and black pepper to the vegetables. Stir until the mixture is thick and well combined.
Incorporate the Rice: Fold in the cooked white rice. Use your hands or a stiff spatula to blend everything together until the rice is evenly coated with the egg and vegetable mixture.
Shape the Rounds: Scoop approximately 1 tablespoon of the mixture at a time. Roll firmly between your palms to form uniform balls and arrange them on the prepared baking sheet.
Bake to Golden: Place the sheet in the oven and bake for 25–27 minutes. The balls should be firm to the touch and a light golden brown on the outside.
Rest & Set: Allow the rice balls to cool on the pan for 5 minutes before moving them; this help the cheese and egg "set" so they don't break.
Store for Later: Keep any leftovers in an airtight container in the refrigerator for up to 3 days.