Preheat the oven to 400 degrees F. Line a baking sheet with parchment or waxed paper.
Thaw the pastry at room temperature for 20 to 30 minutes before gently unfolding. With a sharp knife, divide the pastry in half, wrap the remaining piece in plastic wrap, and return to the freezer for another use.
Cut the pastry into 4 equal triangles. With the tip of a sharp knife, make a 1/4-inch score on all edges of the triangles, being careful not to cut all the way through. Put them on the prepared baking sheet and brush the tops lightly with the beaten egg. Bake until golden brown, 8 to 10 minutes. Remove from the oven and let cool.
With the tip of a sharp knife, carefully remove the top of each pastry and set aside.
In a skillet over medium heat, combine the butter and flour and cook, stirring slowly and constantly for 2 to 3 minutes, to make a blond-colored roux. Add the onion and garlic and cook, stirring, for 2 minutes. Slowly whisk in the broth and cook, whisking occasionally, until it thickens slightly, about 25 minutes.
Season the crawfish with the Creole seasoning and add to the sauce. Cook, stirring, for 2 to 3 minutes. Add the cream, Worcestershire, and hot sauce. Cook, stirring, for 1 minute, then stir in the green onions.
Spoon equal amounts of the crawfish and sauce into the center of the pastries and top with the pastry tops. Serve warm.
Mix all of the ingredients together and store in an airtight container. Can be stored this way for up to 3 months.