In a bowl mix all the dry ingredients, flour, baking powder, baking soda, salt, and sugar.
Add oil and yogurt to the flour and mix it well, add water as needed to make soft dough will be little sticky. Sprinkle little dry flour over the dough and knead to make smooth dough.
Cover the dough and let it sit for about 3 hours or more.
In a saucepan heat the oil on medium high heat. Add all the sauce ingredients, tomatoes, salt, sugar, pepper, and Italian herbs. Cook for about 3 minutes till most of the water from tomato has evaporated and looks like a chunky sauce.
Use the same pan and sauté the bell peppers, and mushrooms for 2 minutes until most of the moisture has evaporated but still they are crisp. Set aside.
Knead the dough for few seconds and divide into two equal parts and roll them in about 10” circle, if dough start sticking to the rolling pin or rolling surface dust little more dry flour.
Heat the heavy pan skillet over low medium heat, lightly oil the skillet and put the rolled pizza over. Let it cook for about 2 minutes until crust has nicely browned from bottom. Lower the heat to low.
Flip the crust, brush it lightly with oil do it quick spread about half the sauce, cheese and topping. Cover the pan for about 3 minutes and check, cheese should be melted. Lift the pizza little from the side crust should be the nicely brown.