Melt ½ stick butter in a skillet over medium heat. Add garlic and mushrooms and cook for 1 minute. Pour in wine, mix well, and cook until all liquid is cooked off. Turn off heat and set aside.
Unroll phyllo dough. Cut stack in half. Working quickly, place 1 sheet of phyllo dough onto a flat surface and brush lightly with melted butter. Put another sheet of phyllo dough on top and brush with butter. Repeat this until you have 3-4 sheets of phyllo. Do not brush the top top layer of phyllo dough with butter.
Cut the buttered stack into four equal parts (squares). Sprinkle grated parmesan cheese in the middle of each square and place approximately 1 teaspoon of mushroom mixture on top of cheese. Optional: Sprinkle additional parmesan cheese onto mushroom mixture.
Gather each square into a neat little bundle, pinching the neck so that it remains closed when baking. Place bundles on a parchment-lined cookie sheet, pressing lightly so that they're flat on the bottom.
Back at 375 degrees for 10 minutes, or until golden brown. Serve immediately.