In a saucepan, bring rice and water to a boil over high heat.
Cook uncovered for 10 minutes, then reduce heat, cover, and simmer for 20 minutes. Let cool and fluff with a fork.
Preheat oven to 400°F. Grease 36 muffin cups (you’ll need three standard 12-cup tins).
In a large mixing bowl, combine grated potatoes, carrots, celery, ground beef, and eggs. Mix thoroughly using your hands or a sturdy spoon.
Add salt, olive oil, rolled oats, and cooled rice. Stir until evenly combined.
Scoop the meat mixture into each muffin cup, pressing down gently to pack it in.
Bake for 45 minutes, or until the tops are set and browned.
Let the cakes cool for at least 10 minutes. To remove, flip the muffin tin upside down over foil or a tray and tap each cup gently. Serve warm or let cool completely and store.