In a large mixing bowl, combine flour, dry yeat, sugar, and salt.
Pour in 1/3 of warm water mix well to combine. Let it rest for 10 minutes.
Add flour, extra virgin olive oil, and the remaining amount of water.
Combine until you obtain a homogeneous dough.
Transfer the dough onto a floured surface and knead until smooth and elastic.
Spray a clean mixing bowl with extra virgin olive oil, and put in the dough.
Cover with a clean kitchen towel and let it rise until doubled the volume.
Preheat the oven to 375F. Line a baking sheet with parchment paper.
Divide the dough into two equal portions.
Place one portion onto a floured surface and roll it into a 10x16 inch rectangle.
Arrange a layer of sliced pepperoni, along with the cheese.
Brush the sides with beaten egg and gently roll the dough into a tight log.
Transfer it onto the baking sheet and repeat with the second portion of dough.
Brush the logs with beaten egg and cut 4 to 5 slits into the top of each stromboli.
Bake for 25 to 30 minutes.
Remove from the oven and let it cool before serving.
Cut stromboli into thick slices and serve.
Enjoy!