Combine water, oil, sugar, and 1/2 teaspoon salt in a medium mixing bowl.
Sprinkle yeast over mixture, stirring until dissolved.
Gradually add flour, mixing well after each addition.
Turn dough out onto a lightly floured surface, and knead about 4 minutes or until smooth and elastic.
Shape into a ball, and place in a bowl coated with cooking spray, turning to grease top.
Cover and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in bulk.
Coat a 12-inch pizza pan with cooking spray; set aside.
Punch dough down.
Lightly coat hands with cooking spray, and pat dough evenly into pizza pan.
Bake at 425° for 5 minutes.
Combine ground chuck and 1/2 tea spoon salt in a skillet; cook over medium heat until meat is browned, stirring to crumble.
Drain beef well on paper towels.
Spread 1 cup pizza sauce evenly over pizza crust, leaving a 1/2 -inch border around edges.
Sprinkle 3/4 cup mozzarella cheese over top.
Sprinkle meat over cheese on pizza crust; top with mushrooms, green onions, and green pepper, if desired.
Bake at 425° for 15 minutes.
Sprinkle with remaining 1/4 cup mozzarella cheese and Parmesan cheese; bake 5 minutes.
Sprinkle with crushed red pepper, if desired.