And the answer is - smoothies!
I've been played with my blender recently and discovered that blending vegetables with fruits and fruit juices makes consuming vegetables tolerable. Right now I'm drinking a concoction that is apple juice, orange juice, carrots, broccoli, spinach, grapes, and blueberries. Is it amazingly delicious? No, I can still taste a hint of spinach and broccoli. But it's pretty inoffensive. I can't imagine a better way to actually eat broccoli, spinach, and carrots.
A full blender is like 3 pint glasses. That plus a sandwich is my lunch today. It's healthy and fast, and I am full.
You should try it for yourself.