Use a rolling pin to evenly flatten the croissants.
Cut out two sheets of parchment paper to match the size of a baking sheet, trimming off any excess.
Mix the butter and brown sugar until combined. Spread evenly on both sides of each croissant.
Place the croissants on a baking sheet lined with one sheet of parchment paper. Cover the croissants with the second sheet of parchment paper.
Lay another baking sheet on top of the parchment-covered croissants and weigh it down with a heavy skillet or similar object to ensure they stay flat.
Bake for 10 minutes at 400°F. Then, remove the weight, flip the croissants, and bake for another 5 minutes, keeping them sandwiched between the parchment and baking sheets.
For extra crispiness, remove the top layer of parchment paper and baking sheet and broil briefly until they reach your desired level of browning. You can flip them again if both sides need additional crisping.
Transfer to a cooling rack.
In a bowl, combine the cream cheese, butter, pumpkin puree, allspice, vanilla extract, and powdered sugar. Mix until smooth.
Once the croissants have cooled, spread the icing on top, using as much or as little as desired.
