Preheat the oven to 425 degrees F. Line a small baking sheet with parchment paper.
Melt the butter over medium heat in a nonstick stillet. Add the mushrooms and onion. Season with salt and pepper and allow to brown, stirring occasionally. Pour in the apple cider, add the Dijon mustard and sprinkle in the fresh thyme. Stir and allow to simmer for a couple of minutes. Remove from heat and let cool a bit.
Slice the wheel of Brie in half. Spread the mushroom mixture on top and then sandwich it back together. Wrap the puff pastry strips around the Brie to resemble a mummy. Place the wrapped Brie onto the prepared sheet pan.
Bake at 425 degrees F for 25 minutes until golden brown. Serve with crackers and green apple slices. Or whatever sounds good to you.