I have found the answer that parents have been searching for for centuries, or at least since the advent of Cocoa Puffs and Cool-Aid. I will qualify this by saying that it only works if you have more than one kid and if there is some degree of sibling rivalry between them.
Here it is:
Don't put the veggies on your kids' plates. Put a small bowl of veggies on the table between them. I swear this works 2 out of 3 times. All of a sudden it becomes a competition between them. I have actually seen my girls fight over steamed cauliflower! Last night Little A was inhaling edamame so quickly, Adam thought she was going to choke.
You are so welcome for my brilliant insight.