Combine yeast and 2 cups warm water in a 2-cup liquid measuring cup, and let stand 5 minutes.
Combine yeast mixture, 3 cups all-purpose flour, whole wheat flour, next 3 ingredients and, if desired, cheese in a large mixing bowl; add 1/2 cup olive oil. Beat at low speed with an electric mixer until blended, stopping to scrape down sides as necessary. Stir in enough remaining all-purpose flour (about 1/3 cups) to make a stiff dough. (Dough will be smooth.)
Place dough and 1 tablespoon oil in a large lightly greased bowl, turning to coat top. Cover and let rise in a warm place, free from drafts, 45 minutes or until dough is doubled in bulk. Punch dough down.
Turn dough out onto a lightly floured surface, and knead 4 or 5 times. Divide dough in half, and shape into balls. Roll each ball into a 14-inch circle on a lightly floured surface. Place one 14-inch circle onto a lightly floured pizza peel; brush with 1 tablespoon oil, and prick with a fork. Add toppings to pizza dough.
Place pizza gently on floor of brick oven. Repeat procedure with remaining dough circle, and place on floor of brick oven.
Bake each pizza at 500° for 5 to 7 minutes or until browned and bubbly.
Note: To bake in a conventional oven, place dough on a lightly floured pizza stone or baking sheet, and bake at 475° for 10 to 12 minutes.
To freeze: Divide risen dough in half before kneading, and wrap in plastic wrap. Place in zip-top freezer bags; freeze up to 3 months. Thaw overnight in refrigerator.