Preheat the oven to 375°F.
Lightly grease a 12-cup muffin pan with non-stick cooking spray. Set aside.
In a small saucepan, melt the butter over medium heat, stirring frequently. Continue cooking until the butter starts to foam and turns a golden-brown color, releasing a nutty aroma. Remove from heat and allow the butter to cool slightly.
In a mixing bowl, combine the pumpkin puree, cinnamon, brown sugar, salt, and browned butter. Stir until the ingredients are well combined, forming a smooth, spiced pumpkin filling.
Roll out the thawed puff pastry on a lightly floured surface. You want the puff pastry to be in a large rectangle (about 10x12 inches). If needed, use a rolling pin to gently flatten the pastry sheet.
Spread the pumpkin filling evenly across the entire surface of the puff pastry, making sure to leave a slight border along the edges.
Slice the puff pastry in half along its length. Next, cut each of those halves in half again, and then repeat once more. You should end up with 8 equal strips of dough.
Tightly roll each strip into a spiral shape, similar to a snail, and place them into the prepared muffin tin.
In a small bowl, beat the egg to create an egg wash. Brush the tops of each cruffin with the egg wash to help them achieve a golden-brown finish.
Bake the cruffins for 20 minutes, or until they are puffed up and golden brown on top. The layers should be crispy and flakey, and the filling should be bubbly and fragrant.
Allow the cruffins to cool in the pan for about 5 minutes, then transfer to a wire rack to cool completely or enjoy warm. Optional: roll them in a cinnamon sugar mixture.
