Preheat oven to 400° F. Line a rimmed baking sheet with parchment and set aside.
Dust the countertop/work surface and a rolling pin (or clean wine bottle) with flour. Roll dough into a rectangle about 11 inches by 15 inches. TIP: If you find your dough keeps shrinking as you roll it, cover it with a slightly damp towel, and let it rest for 10 to 15 minutes then try again. This is common with elastic doughs like pizza dough.
Beat egg until combined in a small bowl.
Combine butter, garlic, and oregano in a small bowl. Spread all over the rolled dough.
Leaving three inches clear on top of the rectangle (long side) and one inch clear on the other three sides, shingle salami, and cheese on the dough. Top with basil leaves.
Brush the perimeters of the dough with egg wash. Carefully roll into a log, folding in side ends as you roll.
Carefully transfer stromboli onto a parchment-lined baking sheet. Make sure the ends are sealed and tucked.
Brush stromboli with egg washes and sprinkle with extra-dried oregano to garnish. Use the tip of a knife to pierce four slits on the top got venting.
Bake in preheated oven for 20 to 25 minutes until golden brown. Rest at least 10 minutes before slicing and enjoying.