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They are made of compressed wheat gluten (fu). The dough is tinted and rolled out in long sticks and sliced up and baked, so it's sorta like refrigerator cookies or millefiori. The disks start out small & hard with mini panda heads on them and then swell up and get spongy but they stay more or less the same thickness while the faces gets huge. When I was a kid, we didn't have the panda shapes but just tinted fu disks: I would put dry ones in my mouth and they would suck all my saliva up and glue themselves onto my tongue while expanding.
I get the soup mix from a Japanese grocery chain called Mitsuwa; they have US locations that carry a lot more stuff than their website. No idea if it's vegetarian, I'll check the label next time I see it, though.