If you're in Japan, you make them out of rice. At least that's the way they do it at Mos Burger. That venerable fast food joint you'll find all over Japan and several other countries.
I once had a vegetarian pattie in Australia that was sooo good that I've been searching high and low for something similar. I think the Australian ones are sold in grocery store frozen sections.
I ordered the above sandwich from a picture on the menu thinking, perhaps, that the "buns" were made out of the same thing the Australian patties were made from. Umm, no. That one above has deep fried veggies and some kink of seafood. I gave it away.
If you're interested... click here for the Mos Burger Menu.