Preheat your oven to 400°F (200°C).
In a skillet over medium heat, heat the olive oil. Add the mushrooms, garlic, thyme, salt, and pepper. Cook until the mushrooms are tender and their moisture has evaporated, about 5-7 minutes. Let cool slightly.
Roll out the puff pastry on a floured surface and cut into 12 squares.
Place each pastry square into the cups of a mini muffin tin, pressing down gently to form shells.
Fill each shell with the mushroom mixture and top with crumbled goat cheese.
Bake in the preheated oven for 15-20 minutes, until the pastry is golden brown and the cheese is bubbling.
Remove from the oven and allow to cool for a few minutes before serving.