Place oven rack in center of oven and preheat to 400˚F.
Cook Bacon. Remove to paper-towel lined plate.
Lightly flour work surface and unfold puff pastry sheet, rolling it out to a 14" x 14" square. Pinch seams created by folds to seal them together as you roll. Move dough often and dust sticky areas with flour.
Arrange 4 bacon slices in 2 lines from left to right: one across the top, the other across the bottom, leaving 1” border. Between rows of bacon spread scrambled eggs running entire width of bacon lines, but not all the way to edge of dough. Scatter cheese over top.
Beat remaining egg with water and brush around perimeter of dough.
Begin rolling Stromboli by taking the longer side of dough and rolling it over filling. Pinch seam to seal. Place Stromboli on parchment lined baking sheet with seam side down. Tuck ends under to seal and brush entire roll with egg wash. Sprinkle dough with salt and pepper to taste.
Bake for 25−30 minutes, or until crust is deep golden brown. Let sit for at least 5 minutes before slicing. Serve hot.