In a food processor, mince mushrooms.
In a 10- to 12-inch frying pan, combine mushrooms and butter. Stir often over high heat until juices evaporate and mushrooms start to brown, 5 to 7 minutes.
Lay pocket bread rounds cupped side up on a baking sheet and scatter the mushroom mixture equally on top of them. Sprinkle each with about 3 tablespoons cheese.
Bake in a 400° oven until cheese melts and bread crisps, 5 to 7 minutes. Drizzle chutney over each pizza and cut each round into quarters.
Nutritional analysis per piece.