Preheat oven to 210 C (410 F) and line two mini muffin trays with paper muffin cups.
Cook rice according to packet instructions so you have 1 cup of cooked rice (my rice required 1/2 cup of uncooked rice to make 1 cup of cooked rice. Check packet because different variations of rice will swell more than others when cooked).
Meanwhile, boil or steam peas, corn and carrots together until tender.
Combine rice and vegetables together in a mixing bowl.
Allow to cool before adding eggs (so the eggs don't cook from the heat). Once cool, add eggs and half of the grated cheese (so 1/4 cup). Mix until combined.
Put spoonfuls of the mixture into the prepared muffin trays, filling each muffin cup about 3/4 full.
Sprinkle the remaining grated cheese on top of each one.
Bake for 20 - 25 minutes, or until firm and golden on top.