Melt 1/2 stick butter in a skillet over medium heat. Add garlic and mushrooms and cook for 1 minutes. Pour in wine, stir to mix, and cook for five minutes, or until all liquid is cooked off. Turn off heat and set aside.
Unroll phyllo dough. Cut stack in half. Working quickly, place 1 sheet on a flat surface and brush lightly with melted butter. Place another sheet on top and brush with butter. Repeat this until you have four to five sheets of phyllo. Do not brush top layer with butter.
Cut this buttered stack into four equal squares (rectangles). Place a spoonful of mushroom mixture in the middle of each square. Sprinkle Parmesan over the top of each mushroom.
Gather each square into a neat little bundle, pinching the neck so that it remains as closed as possible when it bakes. Place bundles on a greased or parchment-lined cookie sheet, pressing lightly so that they're flat on the bottom.
Bake at 375 degrees for 15 minutes, or until golden brown. Serve immediately.