In a 2- to 3-quart pan under cover, boil rice in water with 1 teaspoon salt until very tender, about 1-½ hours. The rice must cook to a mush, and never mind the extra water. It’s also very important that the beef, the rice, and the water it is cooked in are really cold at preparation time. Transfer the rice with its liquid to a chilled dish and refrigerate until cold (or place in the freezer after cooling slightly). Keep the beef in the refrigerator also.
Measure cooked rice and liquid, and if necessary add enough ice water to make 3 cups. Pour over ground beef in a large bowl. Add the egg, ½ teaspoon salt, pepper, and paprika, and work ingredients together until completely mixed. Cover with plastic or aluminum foil and refrigerate 2 hours or longer. (This much of the recipe you can do in the morning or even the night before.)
Transfer the chilled mixture to a flat surface and form it into an oblong piece about 1-inch thick. With a wet knife, divide it into 1-inch pieces. With wet hands, roll pieces into the shape of olives or little sausages. Chill again.
About 30 minutes before serving, fry pieces 2 to 3 minutes in a heavy skillet in a very small amount of hot oil or shortening, just enough so that the meat won’t stick to the pan. Or bake at 450 degrees F for 12 to 15 minutes. Don’t overcook.
Serve with fluffy mashed potatoes and a big salad. Any kind of sauce will help the “olives” if you use them as a main course, which serves 8, but if you want to be authentic, try the sweet-and-sour sauce also adapted from a Martha Washington recipe.
Melt the butter in a heavy saucepan over medium heat. Add flour in small sprinklings, stirring constantly with a wooden spoon. Let mixture bubble, then remove from heat and gradually stir in broth. Add vinegar, sugar, and parsley, return to medium heat, and bring to a boil.
Immediately reduce heat and simmer, stirring, for 3 to 4 minutes. Add capers or olives, if you like, before serving.
If you like a thinner sauce, add 2 to 3 tablespoons more broth or water. If you like a thicker sauce, cook a couple of minutes longer.
This simple, basic, very old-fashioned sauce is also good with a few tablespoons of white wine instead of vinegar. If the white wine is sweet, use less sugar or omit it altogether.