Preheat an oven to 400 degrees F (200 degrees C). Lightly grease a baking tray.
Lay puff pastry out on a lightly floured surface and cut into 8 squares. Prick the squares in several places with a fork. Place the puff pastry squares on prepared baking sheet.
Bake the puff pastry squares for 7 minutes. Remove tray from the oven, flatten the squares using the backside of a spatula. Return puff pastry to the oven to bake until golden brown, 5 to 8 minutes. Remove from oven.
Meanwhile, melt butter in a skillet over high heat. Cook and stir the mushrooms and garlic in the butter until mushrooms are tender, 5 to 7 minutes. Remove from heat.
Top the baked puff pastry squares evenly with the mushroom mixture. Crumble goat cheese over mushrooms and sprinkle with parsley.