In a large bowl, sift the all-purpose flour, then add the dry yeast, salt, and sugar. Mix well.
Pour in the lukewarm water and olive oil, then start kneading. Work the dough until it is smooth and elastic, then cover and let it rise for 1 hour.
Cut the bell pepper and chili pepper into thin slices.
Divide the risen dough into two parts, then roll them out into circles on a floured surface.
Spread the tomato sauce on one half of each dough circle, then sprinkle with the grated cheddar and mozzarella cheese.
Arrange the pepper slices on top of the cheese, then season with oregano, basil, and a pinch of black pepper.
Fold the other half of the dough over the filling, then press the edges together to seal the calzone.
Brush the top with beaten egg, then use a fork to prick a few holes to allow steam to escape during baking.
Bake in a preheated oven at 400°F (200°C) until golden brown, about 20 minutes.
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