Combine first 3 ingredients in a large mixing bowl; stir well. Combine olive oil and water in a saucepan; heat to 120° to 130°.
Gradually add liquid mixture to flour mixture, beating well at low speed of an electric mixer. Beat 2 additional minutes at medium speed.
Sprinkle 2 tablespoons bread flour evenly over work surface.
Turn dough out onto floured surface, and knead until smooth and elastic (about 10 minutes). Place in a bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 45 minutes or until doubled in bulk.
Sprinkle remaining 1 tablespoon bread flour evenly over work surface. Punch dough down; roll to a 14-inch circle on floured work surface. Transfer dough to a 14-inch pizza pan coated with cooking spray and sprinkled with cornmeal. Set aside.
Combine mushrooms and next 3 ingredients in a large bowl. Add garlic-flavored olive oil; toss well. Add oregano and next 3 ingredients; stir well. Arrange vegetable mixture evenly over pizza crust; sprinkle cheese evenly over vegetables. Bake at 425° for 15 to 20 minutes. Cut into wedges.