Preheat oven to 425°F. Grease a 24-well mini muffin pan.
In a large frying pan, over medium-high heat, melt the butter. Add the mushrooms, garlic, shallot and thyme. Cook for 8 minutes.
Add the wine and cook for another 3 minutes or until the wine is reduced. Season with salt and pepper. Set aside to cool.
Roll out the puff pastry. Cut each sheet into 12 squares. Fit the pastry squares into the wells of the muffin tin. Evenly divide the mushroom mixture into each. Add cheese to the top of each. Fold the pastry corners over the mushroom mixture. Brush the tops with the egg wash.
Bake for 20 minutes or until golden brown. Cool slightly on a wire rack and serve warm.