Preheat oven to 400 and remove puff pastry from freezer to allow it to come to room temperature.
Start by making your pumpkin brown butter by heating butter on medium to low heat. Stir and it should start to brown and be golden after about 5 min.
Add the butter to a bowl and whip over ice until it hardens, about 5-8 minutes. Before it gets too hard, add pumpkin puree and pumpkin spice and combine.
Roll out puff pastry and cut out a square that is big enough to fully wrap around the brie. I made mine a little larger to be safe, you can always remove excess once you wrap.
Once it’s still pliable but firm, add a small dollop of the pumpkin brown butter to the center of the puff pastry square. Add brie to the center and pull the sides of puff pastry to the middle until fully covered. Brush with egg wash to help keep it closed.
Using kitchen twine, wrap (similar to a present) each bun into the shape of a pumpkin (4 pieces of twine/ yielding 8 wedges of pumpkin). Using scissors, snip off the loose ends of the twine.
Spray cocottes with cooking spray and add brie pumpkins. Brush with egg wash and bake for about 25 min or until the top is golden brown and the brie is bubbling. Let cool slightly and remove from cocotte. Cut twine and top with cinnamon stick. Serve with whatever fixins you want!