In a large bowl, combine the flour, salt, sugar, and dry yeast. Add the lukewarm water and olive oil, then knead until you have a soft, elastic dough. If it's too sticky, add a little flour; if it's too dry, add a little water.
Cover the dough and let it rise in a warm place for about 1 hour, or until doubled in size.
Grate or crumble the cheeses, then mix them together in a large bowl with the minced garlic and oregano.
Turn the risen dough out onto a floured surface and divide it into four equal portions. Roll each portion into a circle approximately 3 mm thick.
Pile the cheese mixture onto one half of each dough circle, leaving about 1 cm of space around the edges for folding.
Fold the dough over to create a half-moon-shaped calzone. Press the edges firmly to seal, then use a fork to crimp the edges to prevent them from opening during baking.
Brush the top of each calzone with a beaten egg to give it a golden brown color after baking.
Bake in a preheated oven at 400°F (200°C) for about 20 minutes, or until the calzones are nicely golden brown.
Let cool slightly, then serve fresh, possibly with extra Parmesan cheese or a garlic dipping sauce.
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