In a large bowl, sprinkle the yeast along with the sugar. Add the warm water and mix gently. Cover and let it proof for about 5 minutes. If the yeast is active and good, it will bubble and froth. Now add the olive oil, salt and 3 or more cups of flour. Mix well to form a soft dough and knead for about 2 to 3 minutes. Place the dough in a greased or oiled bowl, roll it to coat with the oil. Cover the bowl and place in a warm place to rise until doubled, about 2 hours
Now in a pressure cooker, place the tomatoes, onions, and green chillies and give one whistle. Remove and blend it to a smooth paste with the garlic. Pour this into a deep pan, add the tomato puree or paste, salt, oregano and Italian seasoning, mix well and bring to boil. Once it comes to a boil, lower the heat and simmer for about 20 minutes.
Preheat the oven to 400 degrees Fahrenheit or 200 degrees Centigrade. Take 2 inch balls of the dough and roll into a medium thin circle. On one-half of the circle, layer the bell pepper, onions, mushrooms, green chillies, olives and cheese.
Divide the fillings among the calzones. Fold the other half of the dough over the filling and seal the edges. Place the uncooked calzones onto greased baking sheets and bake in the preheated oven for about 15 minutes till they are well baked and light golden brown.
You can brush the top of the calzones with any olive oil before baking; these give a brown crust. Serve these warm calzones with the hot prepared sauce on the side.