Melt the butter in a medium saucepan or large skillet over medium heat. Add the apples, brown sugar, cinnamon, and nutmeg. Cook, stirring frequently, for 5 to 7 minutes or until the apples begin to soften. Set aside.

Unfold the puff pastry onto a lightly floured surface, and use a rolling pin to smooth out the creases in the sheets. Use a knife to cut off the top 2 corners of each sheet. Cut 8 to 10 (1-inch wide) slanted strips on each side of the pastry sheets. Cut off the 2 remaining strips at the bottom of each sheet.

Divide the apple filling in half and spread it down the center of each pastry.

Fold the strips over the filling, alternating sides with each strip to create a braid. Fold in the ends, and gently press to seal the filling inside.

Transfer the pastries to the prepared pan. Brush the beaten egg over each pastry. (You may not use all of the egg.)

Bake for 16 to 20 minutes or until golden brown. Allow the pastries to cool on the pan on a wire rack while making the glaze.

Whisk together the confectioners’ sugar and milk until smooth. Drizzle over the pastries before serving.