In a large bowl, combine the flour, yeast, and salt. Add the olive oil and lukewarm water, then knead until you have a soft but not sticky dough. If the dough is too dry, add a little more water, a tablespoon at a time.
Cover the dough with a clean kitchen towel and let it rise in a warm place for about an hour, or until doubled in size.
While the dough is rising, dice the tomato and black olives, then shred the mozzarella and Parmesan cheese.
Crumble the feta cheese, then mix it with the shredded cheeses, tomato, olives, oregano, and fresh basil.
Once the dough has risen, divide it into two equal portions. Roll each portion into a circle, about 5 mm thick.
Spoon the feta filling onto one half of each circle of dough. Fold the other half over the filling, and press the edges firmly to seal, ensuring no filling leaks out.
Preheat your oven to 400°F (200°C). Brush the top of each calzone with beaten egg to give it a beautiful golden brown color.
Place the calzones on a baking sheet lined with parchment paper and bake for 20-25 minutes, or until golden brown.
Let the calzones cool for a few minutes before slicing, to prevent the filling from spilling out while it's too hot.
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