Here is the tough part about veggie burgers - getting them to stay together.
Some people use egg white as a binder.
That works, but it can result in a loose, less firm patty.
In those instances, grilling becomes harder than frying or baking.
And vegans are left out of the fun.
One trick for a firmer burger is to use overcooked/mushy grain or pasta as a binding agent.
Just mix soft rice or pasta (a macaroni, penne, etc., shape works better than spaghetti) in with your vegetables to keep the whole thing together.
If you want, you can puree the binding agent of choice with or without some of the other vegetables before mixing them all together.
Then cook on the grill, on the stove, in the oven or by nuking.
Works like a charm.
What veggies to use?
Dealers choice. Cut and dice whatever and for you omnivores, you can add some pieces of meat. Just make sure that it is cooked thoroughly.
One way to better your chances of properly cooked meat is to add pre-cooked pieces to the patty.
That way, the veggies are not overcooked, the meat is not undercooked and the whole thing gets nice and hot.
If you are short on rice or pasta, a plain mashed potato will work, too. Try a sweet potato for variety.