Put the rice in a heavy bottom saucepan, and add cold water, bouillon cubes, and the pat of butter. Bring to a boil over high heat. Immediately, give one stir and cover. Turing the heat to low. (As low as possible) Leave the pan on the burner for 20 minutes without stirring or opening the pan. After 20 minutes, open pan, and fluff rice with a fork. Rice for this dish should be slightly sticky. If rice is too dry or fluffy, add a tablespoon of water, and place back on low heat for a few more minutes. When rice is thoroughly cooked and sticky, let covered pan cool to room temperature.
While rice is cooling, cook hamburger in an open frypan until it is thoroughly cooked. Crumble cooked hamburger finely. Drain cooked hamburger in a colander and discard fat.
Mix cooled rice, hamburger, cheeses, and melted butter. Taste mixture and correct seasonings by adding salt and pepper to taste. (I use a lot of pepper, some people add a little oregano here.) Add beaten eggs, and then mix thoroughly. You want the mixture to be about the consistency of play dough, albeit lumpy.
Mold the mixture into small balls, about 1-1/2 inches in diameter. You will need to have wet hands to do this. If youve ever made meatballs, the process is similar, but you kind of have to press the rice to make it hold together. Let the finished balls sit out for 15 minutes or so to firm up.
Roll the rice balls in flour, then egg wash, then breadcrumbs. Again, let sit out for a few minutes for the coating to firm up on the rice balls.
Preheat oil in deep fryer to 300 - 325 degrees. Fry the rice balls a few at a time, until very lightly colored. Place fried rice balls on cookie sheet, sprayed with Pam. When all the rice balls are fried, bake in a 350 oven for 20 minutes or so. This is to make sure that the egg is completely cooked, and to prevent salmonella poisoning.
Rice balls can be refrigerated for 3 - 4 days, and served warm. A little tomato sauce on the side for dipping is very good, too.
BTW, this is not as much work as it appears to be. Cooking the rice is largely unattended, and a batch normally takes me an hour, once the rice is cool.
Using leftover grains or standard pantry rice requires careful moisture control. Regular long-grain starches lack the natural amylopectin found in Italian arborio, which means the binding phase relies entirely on added eggs, melted butter, and shredded cheddar to hold the mass together. Letting the cooked rice cool completely before mixing prevents the eggs from prematurely curdling on contact with hot starch. Keeping palms damp during the shaping stage stops the sticky mixture from tearing apart while forming uniform spheres. Maintaining oil temperatures between 300 and 325 degrees Fahrenheit ensures the exterior browns gently without burning the delicate crumb crust before the interior warms through. Frying batches too heavily will drop the oil temperature and create a greasy, saturated shell. A final twenty-minute bake at 350 degrees solidifies the interior structure completely. Storing leftovers in the refrigerator for three to four days maintains food safety while preserving the crunchy textural contrast.