Beat egg. Stir in the buckwheat groats, and coat them thoroughly.
Heat a frying pan over low to medium heat. Put the buckwheat/egg mixture in the dry pan. Stir it around, breaking up clumps, until the individual grains are separate and the egg is cooked.
Add the broth, stir.
Cook for 20-25 minutes, until the liquid is absorbed and the grain is tender.
If desired, add sauteed onion, sauteed mushrooms, or both.