Line a rimmed baking sheet with parchment paper. Set aside.
In a large saute pan heat olive oil and butter over medium heat. Add shallot, garlic and cook until softened. Add mushrooms. Season with salt, pepper and thyme. Add wine and cook until wine has completed reduce and mushrooms are cooked through. Set aside to cool slightly.
Cut each puff pastry sheet into 9 equal portions.
To assemble: Place a slice of brie into center of each puff pastry square. Top with a spoonful of mushroom mixture. Fold pastry into a triangle. Seal using a fork. Transfer to baking sheet. Continue with remaining squares.
Bake for approximately 20 minutes or until pastry is golden.