Combine yeast, sugar and warm water and let set for 5 minutes. Mix remaining ingredients and then add yeast mixture. Let dough rise, in a warm place, for about 30-45 minutes.
In the meantime, peel zucchini if desired, and de-seed bell peppers. Put zucchini, bell peppers and mushrooms in a food processor or blender and pulse until blended. Stir in 1/2 cup of shredded mozzarella cheese into the veggies.
Roll out a small portion of the dough at a time, for mini calzones we use a golf ball size. Roll or press out. Fill middle with filling: thin layer marinara sauce, and a scoop of veggies. Fold calzone in half and then crimp edges with a fork. Set on baking tray.
Whisk 1 egg white in a small bowl. With a pastry brush, brush the top of the calzone.
Bake at 425 for 10-15 minutes until lightly browned. Test to make sure dough is done baking by tapping on it. It should sound hollow.
Let cool slightly and serve with marinara sauce for dipping.