Sift the flour into a large mixing bowl, add the salt, and mix. This helps achieve a smooth and consistent dough.
Dissolve the yeast in the warm water, then add it to the flour. Pour in the olive oil and begin to combine the dough.
Knead the dough until it is smooth and elastic. If it's sticky, you can add a little flour, but not too much, as it may dry out the dough.
In a lightly oiled bowl, let it rise covered for about 1 hour, or until doubled in size.
Slice the red onions thinly. In a skillet over medium heat, heat some olive oil, then add the onions and sauté slowly.
When the onions are translucent, add the brown sugar and balsamic vinegar, then continue to sauté until the onions are caramelized and deep brown in color.
Mince the garlic and stir it into the caramelized onions. Add the freshly chopped thyme and black pepper.
Grate the mozzarella and smoked cheese, then mix them with the caramelized onion mixture.
Punch down the risen dough on a floured surface, then divide it into 4 equal parts, and roll each into a circle.
Evenly distribute the filling on one half of each dough circle, being careful to leave the edges free.
Fold the dough over the filling, press the edges together, and then use a fork to seal them tightly, so they don't open during baking.
Place the calzones on a baking sheet lined with parchment paper, then brush with beaten egg to give them a beautiful golden-brown color.
Bake in a preheated oven at 400°F (200°C) for about 20-25 minutes, or until golden brown.
Let the baked calzones rest for a few minutes, then serve warm.
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