This comes from my brother Matt. I fell in love with them the first time he made them for us!
Reconstitute the mushrooms in water. Don't use too much water, to avoid leaching the mushrooms. They should be ready within an hour.
If starting with whole mushrooms, julienne them with a knife or a 3 mm food processor julienne blade (or just slice them if you prefer). Melt half the butter in a pan and begin sautéing the mushrooms. Wait until all of the butter has been absorbed before adding the rest, to ensure that it is evenly absorbed. Sauté the mushrooms on high heat until they are slightly browned. Turn off the heat and add sake (½ to 1 cup depending on taste) while continuing to stir.
Fresh shiitake mushrooms can also be used, but they are not as flavorful, are much harder to julienne, and cook down much more.