Preheat oven to 375 degrees. Line a baking sheet with parchment or a silpat liner.
Heat 1 tablespoon of olive oil n a large skillet over medium-high heat. Add in sausage and cook, breaking up clumps with a wooden spoon. Cook until lightly browned, about 10 minutes. Remove with a slotted spoon and place in a bowl to cool.
Wipe out the frying pan with a paper towel and place it back onto the stove. Heat remaining oil over a medium low flame and add in peppers and onions. Cook, stirring periodically until softened, about 8 minutes. Remove from the heat and allow to cool.
On a lightly floured surface, roll out your dough into a large circle, approximately 12 inches in diameter.
Place 3 slices of cheese overlapping towards the bottom third section of the dough. Top with 1/3 of the sausage mixture and 1/4 of the peppers and onions.
Fold in the sides and the bottom of the dough to cover the filling and roll it over once. Repeat the process two more times working with the remaining thirds until all of the ingredients are used up.
Roll it up tightly, run a little water on the edge of the end of the dough before sealing and pinch the seam tightly to seal. Place the entire Stromboli onto prepared baking sheet, seam side down.
Brush with egg wash and bake in oven until golden brown, approximately 25-30 minutes.
Allow to cool on baking sheet for 5-10 minutes before slicing (on the bias) into 1-inch pieces.