To make the filling: In a large skillet over medium-high heat cook Italian sausage and onion in a couple of drizzles of olive oil. Cook until no pink remains then, drain any excess fat from the pan.
Add minced garlic, Italian seasoning and red pepper flakes. Cook for an additional 1-2 minutes. Taste and add salt to your personal taste.
Remove from skillet from heat mixing in Italian parsley. Set aside to cool.
Preheat the oven to 400°F and line a large 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-size mixing bowl.
In a separate bowl, add 1 cup of flour, yeast, sugar, salt and olive oil. Add warm water. mixing until fully combined and the yeast has dissolved.
Add the wet ingredients to the flour in the other mixing bowl. Mix together with a large silicone spatula until fully combined. The dough will be sticky.
Turn dough out onto a lightly floured surface turning to coat with flour until it's not sticky.
Knead for 3-4 minutes adding flour as needed. [not to exceed 1/2-3/4 cup total]
Flatten the pizza dough pressing to roughly a 14 x 19-inch rectangle.
Sprinkle dough with 1/2 shredded cheeses (equal parts) over dough then top with cooked sausage leaving a 1-inch border around the edges. Brush the border with the beaten egg wash.
Sprinkle with remaining shredded cheese and 2 Tbsp Parmesan cheese. Begin to roll from the widest side. (Don't panic if the dough tears, it will repair 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 sprinkling remaining Parmesan cheese.
Reserve some butter to brush on top after removing from the oven.
Bake at 400° F for 30-35 minutes or until golden. Rest for at least 15 minutes on the counter before cutting.
Slice into 1-inch slices, and serve as is or with pizza sauce or cheese for dipping.