To make the filling, cook the finely diced onion in a couple of drizzles of olive oil until translucent, seasoning with salt and black pepper to taste. Add the ground Italian sausage and cook until no pink remains, then drain any excess fat from the pan.
Add the Worcestershire sauce, minced garlic, Italian seasoning and red pepper flakes. Cook for an additional 2 minutes.
Remove from the heat and add the chopped Italian parsley. Set aside to cool.
Preheat the oven to 400°F and line a baking sheet with a silicone baking mat or parchment paper.
To make the pizza dough: Divide the flour. placing 2 1/2 cups in a medium mixing bowl.
In a separate bowl, add 1 cup of flour, yeast, sugar, salt and olive oil. Add the water. and mix until fully combined and the yeast has dissolved.
Add the wet ingredients to the flour in the other mixing bowl.
Mix until combined, then turn out onto a floured surface. The dough will be sticky.
Knead for 3-4 minutes adding flour as needed. [not to exceed 1/2-3/4 cup] Shape into a ball.
Flatten the pizza dough pressing to roughly a 14 x 19-inch rectangle.
Spread the sausage over the dough leaving a 1-inch border around the edges. Brush the border with the beaten egg wash.
Sprinkle with the shredded cheese. Begin to roll from the longest side. Don't panic if the dough tears, dough has a way of repairing itself when baking and the cheese will act as a tasty glue.
Place seam side down on the baking sheet, shape and tuck the ends under to seal.
Brush the top and sides with melted butter, and sprinkle with garlic salt and grated Parmesan cheese.
Reserve some butter to brush on top after removing from the oven.
Bake at 400° F for 30 minutes or until golden. Rest for 10 minutes on the counter before cutting.
Slice into 1-inch slices, and serve as is or with marinara sauce for dipping.