Peel and halve the onions. Parboil in salted water for 12 minutes. Remove centers, leaving about 3/4" edges. Place onion cups in a 13x9x2" pan.
Chop the center portions which were removed from the onions to equal about 1 cup.
Cook broccoli to package directions; drain.
Combine chopped onion, broccoli, Parmesan cheese, mayonnaise and lemon juice; spoon into the onion cups.
Note: at this point the onions can be refrigerated until ready to bake.
Melt butter; blend in the flour, salt, pepper and garlic powder (if using). Add milk and cook until thick, stirring constantly.
Remove from heat and blend in softened cream cheese. Spoon sauce over the onions; bake, uncovered, at 375°F. for 20 minutes.