Preheat oven to 200 C / Gas 6. Grease three 12-hole muffin tins.
In a medium saucepan, combine the rice with water. Bring to the boil over high heat, uncovered, and cook 10 minutes. Reduce heat to low, cover, and simmer 20 minutes. Remove from heat, let cool several minutes, then fluff with a fork and set aside.
In a large bowl, combine the potatoes, carrots, celery, beef, and eggs. Mix ingredients together using your hands or a sturdy spoon. Add salt, olive oil, rolled oats, and rice; mix well.
Fill each muffin hole with some of the meat mixture, and pat down the to make it firm.
Bake in the preheated oven for 45 minutes, or until surface feels set. Cool on a cooling rack 10 minutes or longer.
Remove the meat cakes by turning the muffin tin upside down over a sheet of tin foil. Tap each muffin hole to release the cake. Store in the fridge or freeze in sealed plastic bags. NOTE: Do not feed to dogs while still hot.
Further nutrition guidance
Supplement your dog's food with the correct ratio of calcium to phosphorous in addition to varying protein sources (including organ meat), fresh fruits and vegetables. It is also good practice to provide a daily multivitamin to dogs along with omega-3 fish oils and a pro-biotic. The following are toxic to dogs even in small amounts: onions, avocados, chocolate, macadamia nuts, garlic, grapes, raisins, apple pips and yeast dough.