In a small bowl, dissolve yeast in warm water. Add the Parmesan cheese, oil, sugar, basil, salt, all-purpose flour and 3/4 cup whole wheat flour. Beat until smooth. Stir in enough remaining whole wheat flour to form a soft dough (dough will be sticky).
Turn onto a lightly floured surface; knead until smooth and elastic, 6-8 minutes. Cover and let rest for 10 minutes.
Roll dough into a 16-in. x 12-in. rectangle. Transfer to a baking sheet coated with cooking spray; build up edges slightly. Prick dough with a fork. Bake at 375° until lightly browned, 8-10 minutes.
Meanwhile, in a large saucepan, bring 1/2 in. of water to a boil. Add spinach; cover and boil until wilted, 3-5 minutes. Drain and place in a food processor. Add pesto; cover and process until blended.
Spread over pizza crust. Top with broccoli, green pepper, green onions, garlic and mozzarella cheese. Bake until cheese is melted, 10-12 minutes.