In a large bowl, heat the olive oil over medium-high heat. Add the diced beef and fry for 5 minutes. Add the onions and cook, until the onions are soft.
Peel the tomatoes (instructions here) and blend in a blender or food processor with ½ cup water until smooth.
Add tomato puree to the meat mixture, cover and simmer until most of the liquid is evaporated and the sauce is thickened. Season the meat sauce with salt and pepper to taste.
To make the dough
In a large bowl, mix together the flour, salt, olive oil, and water until the dough forms. Transfer to a lightly floured work surface and knead until the dough is smooth, elastic, soft, and doesn't stick to your fingers, about 10 minutes.
Divide the dough into 12 equal pieces and knead them into a ball shape. Cover with plastic wrap and let it rest for 10 minutes.
Working with one piece at a time (keep the rest covered), use a rolling pin to roll the dough into a paper-thin sheet in the shape of the pan you are going to use for baking. In my case, the baking pan has a rectangular shape. It is suggested to use a round shape because it is easier to roll the dough.
Preheat oven to 350 degrees Fahrenheit.
Grease a 10x15 inch jelly roll pan. Place one sheet of fillo into the prepared pan and gently pull up the ends. Brush the sheet with melted butter. Repeat with five more sheets.
Spread the filling on top of sheets to cover completely. Repeat layering and brushing with butter the remaining six fillo sheets. Fold the sides up (see picture).
Brush the top of the pie with the egg wash. Bake the byrek pie until golden brown in color, about 40 to 50 minutes. Serve it warm or at room temperature.
~ Xhulio's Tip ~
If Byrek rises during baking, poke a few holes with a fork during baking for air to escape.
If you want to bake it faster, increase the temperature, but it will not be as crispy.
Mix Greek yogurt with salt and a bit of water for a great beverage that goes perfectly with Byrek.