Start by placing the cream cheese in the freezer for about 15 minutes to firm it up.
Preheat your oven to 400 degrees F (200 degrees C) and prepare a baking sheet by lining it with parchment paper.
Cut the butter into 12 slices and arrange 2 slices vertically in 6 sections on the prepared baking sheet.
Sprinkle 1 tablespoon of brown sugar over each set of butter slices.
Once the cream cheese is partially frozen, slice it into 12 pieces and place 2 slices side by side on top of each brown sugar section.
On a lightly floured surface, roll out the puff pastry gently and then cut it into 6 rectangles.
Carefully press the pastry around each mound of the cream cheese mixture, ensuring to press down slightly on the cream cheese.
Use a fork to crimp the edges of each pastry to seal them.
Brush the tops of the pastries with the beaten egg for a nice golden finish.
Bake the pastries in the preheated oven for 15 to 18 minutes, or until they are golden brown and flaky.
After baking, let them sit on the baking sheet for 10 minutes before carefully flipping them over.
In the meantime, whisk together the confectioners sugar and milk until you achieve a smooth icing.
Drizzle the icing over the pastries as desired.
