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, dice the onion and garlic, then sauté them in a little olive oil in a skillet until translucent.
Add the sliced mushrooms and cook over medium heat until golden brown. Sprinkle with oregano, basil, and white pepper.
Pour in the heavy cream, stir to combine, and cook for another 5 minutes to allow the flavors to meld.
Divide the risen dough into two equal portions, then roll each out into a circle, about 5 mm thick.
Spoon the creamy mushroom filling onto one half of each circle, then sprinkle with the grated mozzarella and Parmesan cheese. Fold the other half over the filling and press the edges firmly to seal, preventing the filling from escaping.
Preheat the oven to 400°F (200°C). Brush the top of each calzone with beaten egg to achieve 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 rest for a few minutes before slicing, to prevent the filling from being too hot and runny.
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