Why use vegetables instead of potatoes?
These have a lot more flavor than just potato latkes, and they're less fattening too. My kids like vegetable latkes so much that I make them even when it's not Hanukkah. I also often make them for company, when the company involves a lot of allergies and food restrictions, because nobody's allergic to vegetables, and the only other thing in these is eggs and a tiny amount of flour. If there's a gluten issue, you can easily substitute gluten-free rice flour for the wheat flour.
How to make vegetable latkes:
In a food processor, grate two carrots, two peeled turnips, and half an onion. You may need to work in batches. Dump all the shredded vegetables into a medium-sized mixing bowl and add 3 tablespoons of chopped parsley, three eggs, three tablespoons of flour, and salt and pepper to taste.
You can fry these latkes in a large frying pan in olive oil, which is more in the spirit of the holiday and I think better too, but it takes longer. Or, you can liberally grease a cookie sheet with olive oil and bake the latkes on that in a 425 F oven. Either way, keep the latkes small - about 2 inches in diameter - or they will break apart. You'll need to turn them to cook both sides; they need about two minutes on each side in the frying pan, and about five minutes on each side in the oven.
Vegetarian or vegan?
This is vegetarian, but it's not vegan, because you need eggs to hold the latkes together.
Can I keep leftover latkes for later?
Yes, these are pretty good reheated the next day, but they're better fresh. You can't freeze them. You can, however, freeze the grated vegetables and eggs uncooked, and then just thaw them and bake them to get latkes. Good to know if you have company coming and you don't want to be running noisy food processors.