In a large bowl, combine the flour, yeast, and salt. Add the olive oil and lukewarm water, and 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.
Mince the garlic and sauté it in olive oil over low heat until fragrant, being careful not to burn it.
In a bowl, combine the plain yogurt with the sautéed garlic, black pepper, oregano, caraway seeds, and smoked paprika.
Divide the risen dough into two equal portions. On a lightly floured surface, roll each portion into a circle about 5 mm thick.
Spread half of the yogurt-spice mixture onto one half of each dough circle. Top with grated mozzarella and Parmesan cheese.
Fold the other half of the dough over the filling and crimp the edges tightly to seal.
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 cool for a few minutes before slicing and serving, to prevent the filling from being too hot.
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