Rice-Hash Cakes

Preheat oven to 350 degrees F. Melt the butter in a saucepan . When hot and bubbly, and the onion, carrot and celery . Cook until the vegetables begin to soften. Add the beef , potato and mushrooms and cook for an additional 4 minutes. Transfer the mixture to a bowl, mix in the rice , sprinkle with the flour and then with the broth . Mix in the egg. Sprinkle with salt and pepper. Lightly butter a baking sheet. Using a lightly oiled bowl for a mold , pack about 1 1/2 cups of the mixture into a lightly oiled small bowl and turn out onto the baking dish. Repeat 3 times for 4 hash cakes. Alternatively, these can be hand shaped. Lightly dusted with additional flour and sauteed in your grandmother's heirloom cast iron skillet.