Slice the mushrooms into rings about 1/4 inch thick. Heat a large frying pan over high heat for 2 minutes, then lay the mushroom rings down in the pan -- dry. Shake the pan a bit to keep the mushrooms moving (they will squeak). Turn the heat down to medium-high and keep shaking the pan often until the mushrooms begin to release their water.
After the water has been sizzling out of the mushrooms for a minute or two, you will hear the sizzle sound change. When you hear this, add the butter and swirl the pan to coat. Toss a little salt in, too -- maybe a teaspoon or so.
Toss the mushrooms to evenly coat them with the butter and cook on medium heat until the edges of both sides brown. Remove and serve immediately.