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 it's too dry, add a little more water.
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, prepare the filling: grate the smoked cheese, mozzarella, and Parmesan, then chop the cooked ham.
Combine the cheeses with the ham, oregano, and basil, ensuring the filling is well mixed.
Divide the risen dough into two equal portions, then roll each out into a circle, approximately 5 mm thick.
Spoon the smoked cheese mixture onto one half of each dough circle, then fold the other half over the filling. Press the edges firmly to seal and prevent the filling from escaping.
Preheat the 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 them cool for a few minutes before slicing, to prevent the filling from being too hot and runny.
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