Preheat the oven to 350°F (175°C). Line a small to medium baking sheet with parchment paper or a silicone baking mat.

Place one puff pastry sheet onto the prepared baking sheet. Bake for approximately 10 minutes, or until the pastry is just set but not browned or flaky. This par-baking step helps prevent a soggy bottom crust. Remove from the oven and set aside.

In a skillet over medium heat, cook the ground sausage until fully browned. Do not drain the rendered fat. Reduce the heat to medium-low, add the flour, and stir continuously until the mixture begins to bubble, forming a roux. Gradually add the milk and black pepper, stirring until a thick sausage gravy forms. Remove from heat and evenly spread the gravy over the par-baked puff pastry. Wipe out the skillet for reuse.

In the same skillet, cook the shredded hash browns until golden and crisp on both sides, adding olive oil sparingly if needed to prevent sticking. Spread the cooked hash browns evenly over the sausage gravy layer.

In a small bowl, beat the egg. Drizzle approximately half of the beaten egg over the hash browns. Brush the exposed edges of the bottom puff pastry with a small amount of the remaining egg wash.

Evenly distribute the cooked bacon over the layered filling. Arrange the cheese slices evenly on top of the bacon.

Carefully place the second puff pastry sheet over the filling. Press the edges together to seal, then crimp all sides with a fork. Brush the top of the pastry with the remaining egg wash.

Bake for 18 to 23 minutes, or until the pastry is golden brown and fully cooked. Allow the pastry to cool for 5 to 10 minutes before slicing into 9 bars. Serve warm.