For a vegetarian burger option, nothing beats a potato patty burger done to perfection. It's incredibly simple, essentially just mashed potatoes formed into a patty, breaded and fried. It can be seasoned to your liking with herbs, garlic, salt, etc. and the traditional burger toppings nicely compliment it. You can somewhat emulate it by replacing a burger patty with the fries that often come with an order but it's not the same as a purpose made one.