In a large nonstick skillet, cook the onions, sugar and salt in oil over low heat for 40 minutes or until onions are softened and liquid has evaporated. Reduce heat to medium-low; add hash browns. Cook 8-10 minutes longer or until potatoes are golden brown. Remove from the heat and set aside.
To make crust, unroll breadstick dough onto a lightly floured surface and separate into strips. Pinch several breadsticks together, end to end, forming a rope. Holding one end of rope, loosely coil dough to form a circle. Add remaining breadsticks to coil, one at a time, pinching ends together. Tuck end under; pinch to seal. Cover and let rest for 10 minutes.
Roll into a 10-1/2-in. to 11-in. circle. Transfer to an ungreased 9-in. pie plate. Spoon onion mixture into crust. Top with broccoli and cheese.
In a large bowl, whisk the eggs, egg whites and milk; pour over cheese (pie plate will be full). Bake 350° for 40 minutes. Cover edges with foil. Bake 10-12 minutes longer or until a knife inserted near the center comes out clean. Let stand for 10 minutes before cutting. Yield: 6 servings.