Preheat oven to 400 degrees and line a baking sheet with parchment paper. Place a skillet over medium heat and add sausage. Cook sausage, breaking it into small pieces, until it is just no longer pink.

Add the diced onion and bell pepper and cook for an additional 3 minutes. Transfer to a paper towel-lined plate to drain the grease and cool slightly.

Place the hash browns in a medium mixing bowl and pour all but 2 Tbsp of the beaten egg mixture over potatoes. (You’ll use the reserved beaten egg to brush on the pastry.)

Add sausage mixture, Parmesan cheese, salt, pepper and about half of the shredded cheese to the egg/potato mixture, stir to combine and set aside.

Working on a lightly-floured surface, unfold the puff pastry and roll out slightly until you have a 12" x 12" square. Transfer the pastry to the prepared baking sheet. You may need to sprinkle the parchment with a tiny bit of flour to prevent sticking.

Brush a 1" border around the perimeter of the dough with the remaining beaten egg. Place the filling into the center of the puff pastry. Form a 4"-wide line running the entire width of the pastry and leave a 1" border along the left and right sides. You can compact and shape the filling with your hands if necessary. Add the remaining shredded cheese on top of the filling.

Fold the top and bottom flaps of the dough over the filling, overlapping the pastry by at least 1". The egg should help to seal the dough together at the seam. Press the dough on the left and right side together to seal and fold them upward. Roll the entire cylinder over so that the center and side seams are on the bottom of the Stromboli. Re-shape if necessary and then brush the entire pastry with the remaining beaten egg.

Bake 35–40 minutes or until a deep golden brown flaky crust has formed. Cool for 5–10 minutes and cut into thick slices.