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.
If you don't have goat cheese, feta is a rather tasty substitute.