On the recommendations of both enshanam and the waitress, I got the BBQ soy "chicken" sandwich on a French roll.
And it was amazing.
I did not realize lack-of-meat could taste so good. enshanam said the soy was basically a vehicle for BBQ sauce, and that made sense. And there was something about the spongy consistency that made this combination seem more successful than a hypothetical "real" chicken counterpart. Because it doesn't offer much resistance to your teeth, it allows the flavor to mix with everything in the sandwich, so that the focus isn't on the taste of the protein vehicle but the taste of everything else, from the bread to the vegetables to the light spread (mayonnaise? vegennaise? aioli?). The French bread, too, was key, because what kind of a crazy person puts a BBQ sandwich on French bread? The slight crispness balances out the texture of the soy "chicken" in a way that a regular bun wouldn't. It was the best sandwich I'd had in ages.
Perhaps there's more to vegan/vegetarian cuisine than meets the pie.