In a large bowl, sift the all-purpose flour, then add the dry yeast, salt, and sugar. Mix to combine.
Pour in the lukewarm water and olive oil, then start kneading. Work the dough until it is smooth and elastic. Cover and let it rise for 1 hour.
Chop the sun-dried tomatoes into smaller pieces. Thinly slice the black olives.
Divide the risen dough into two equal parts. On a lightly floured surface, roll each portion into a circle.
Spread tomato sauce over half of one circle, then arrange the chopped sun-dried tomatoes and sliced olives on top. Sprinkle with a mixture of grated mozzarella and Parmesan cheese.
Sprinkle with oregano, basil, and a pinch of black pepper.
Fold the other half of the dough over the filling, then press the edges to seal, ensuring the filling doesn't escape.
Brush the top with beaten egg, and use a fork to prick a few holes to allow steam to escape during baking.
Bake in a preheated oven at 400°F (200°C) until golden brown, about 20 minutes.
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