Unroll puff pastry on a flat surface. Roll pastry into a 14-inch square. Using a pizza cutter or a knife, cut pastry into 12 squares.
Top each square with mushrooms (about 1 heaping teaspoon each) and 1 teaspoon grated cheese. Wet 2 edges of each square with wet fingers and then fold over making a triangle. Press the edges together with a fork.
Place turnovers on a large baking sheet, about 2 inches apart. Bake 10 to 12 minutes, until puffed up and golden brown.