In a large saucepan, parboil onions in salted water for 10-12 minutes. Drain.
Cook broccoli according to directions. Drain.
Cut tops off onions. Remove centers of onions (reserve), leaving 3/4-inch edges. Place hollowed onions in baking dish.
Chop onion centers; combine with broccoli, Parmesan cheese, mayonnaise and lemon juice. Spoon into onion shells.
In a medium saucepan over medium heat, melt butter, blend in flour and brown. Add salt and milk. Cook until thickened, stirring constantly. Remove from heat and blend in cream cheese. Spoon over stuffed onions.