Combine Porcini mushrooms, garlic and chicken stock and simmer for 30 minutes. Season to taste with salt and pepper. Meanwhile beat water with egg whites, and gradually, in a thin steady stream, ladle half of the mushroom broth into the egg whites. Pour the mixture back into the saucepan and set over moderate heat. As the broth reaches the simmer, stir it continuously with a whisk. When the simmer is reached, stop stirring; the egg whites should have mounted to the surface in a frothy "cap". Gently move the saucepan to the side (half off heat) so that the edge of the liquid is barely bubbling. Make a quarter turn of the saucepan every 5 minutes until all parts of broth have had a chance to clarify.
Line a wide strainer with a triple layer of washed cotton cheesecloth. Set the strainer over a deep saucepot (so that bottom of strainer remains above surface of liquid). Carefully ladle stock and egg white cap into cheesecloth, disturbing egg whites as little as possible. Towards the end of straining, as cheesecloth gets full, the liquid will pass down more slowly. Just lift the cheesecloth gently so liquid can drain through an unused section of it. Let cheesecloth and egg whites sit over saucepan undisturbed for 5 minutes.
When ready to eat, reheat consomme in a clean saucepan; adjust seasoning and ladle it out. Garnish with raw mushroom slices and radish sprouts.