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, pliable dough. If the dough is 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.
Meanwhile, cook the green peas in lightly salted water for about 5 minutes, then drain and purée with an immersion blender or a fork. Add minced garlic and oregano, then mix well.
Grate the mozzarella cheese and prepare the filling.
Turn the risen dough out onto a floured surface, then divide it into four equal portions. Roll each portion into a circle about 3 mm thick.
On one half of each circle, spread the pea purée and sprinkle with the grated mozzarella. Be sure to leave about 1 cm of space around the edges for folding.
Fold the dough in half 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 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 golden brown.
Let cool slightly, then serve fresh, optionally with extra garlic dipping sauce.
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