Preheat oven to 375 degrees. If using a silicone mini muffin pan, lightly grease the holes with oil. If using a metal muffin pan, grease the holes liberally to prevent sticking.
Make sure to remove any excess moisture from the vegetables you are using by patting dry with a paper towel. Add rice, veggies, egg, egg white, approximately 3/4 of the cheese, and the garlic powder to a large bowl. Mix well.
Fill the muffin tin with the rice mixture, pressing gently on the top of each filled hole with the back of a spoon. Sprinkle a pinch of the remaining cheese on top each each nugget.
Bake until the edges of the nuggets are golden brown, about 15 to 20 minutes. Once cool enough to handle, remove nuggets from the pan. If they are sticking, run a butter knife between the nugget and the pan to loosen. Serve warm with ketchup or other dip if desired.