You know how pastries are injected with filling? Would it be possible to fill an uncut hamburger bun with Sloppy Joe mixture via injection?
And make a Sloppy Joe Bao?
Sure, why not.
Although, it would probably work better on raw dough.
No. You have cut it. Not completely in half, you can insert the knife through a small hole in the side and slice through the interior of the bun to create a pocket to fill.
You’ll need a funnel, a thinnish recipe of S.J. mixture and deft skill.
Yeah, try it.
Can it be done? Sure. Is it worth the effort? That’s the question.
Now that I think about it, it would be best with some kind of roll that’s super fluffy on the inside, and crusty on the outside.
A restaurant I like serves them inside a whole ciabatta. They cut the loaf in half, make incisions all the way through without cutting the crust, and fill it up. Fluffy on the inside, crusty on the outside.
I’ve had a hamburger using pita bread before, so a sloppy joe isn’t so far out. A strike against it though is pita bread isn’t fluffy like a hamburger bun, but it could still be good.
Your scientists were so preoccupied with whether or not they could, they didn’t stop to think if they should.
Put me down for “yes, they should.”
But…if the loose hamburger filling is not spilling out the sides of the unconnected top and bottom bun with every bite, is it just a ‘Joe’?
If you’re going to make it all fancy like that, I believe it’s no longer a Sloppy Joe; it’s more of an Unkempt Jospeh.
Back in the olden days when I was a kid, my mom would buy sub rolls, cut them in half width-wise, scoop out some of the bread innards, and pour the sloppy joes into the void. They were semi-sloppy joes, and with 5 kids, and reduction in clean-up was a win!
At camp they’re knows as Neat Josephs. Perhaps to avoid kids being deliberately sloppy?
My aunt, in a humorous attempt to sound classy, used to call Sloppy Joes “Untidy Josephs”.
Baked bao might work better than steamed here.
I think that that’s what the fussy English butler, Mr. French, called them on Family Affair. 
I’d prefer the sloppy version. We have a variation here in Rhode Island called a Dynamite. The difference, it’s made with tomato paste instead of tomato sauce, with celery salt sprinkled over the meat. It’s hardly even well known here outside of the far northern Woonsocket area though occasionally shows up as far south as Warwick. The locals talk about it like it’s a culinary delight worthy of the Cordon Bleu school compared to a common Sloppy Joe. This state is a weird and wondrous dot on the map.
IMHO, the carb used for this process must be able to absorb a good amount of juice, or then you have an extra-sloppy joe.
I had an aunt who used to make what she called “kraut burgers” She would roll out Pillsbury dough, cut into squares, fill each with a dollop of seasoned ground beef and top with cabbage. Then fold into a pocket and bake. They might not sound appetizing, but they were surprisingly good. I suppose the same could be done with a sloppy joe mixture, although I would think you would want to be careful about not making it too saucy.
Speaking of which, for the love of god, make your own sloppy joes. They are easy and so much better than adding a can of sugary manwich crap to hamburger. Here’s a pretty good recipe. I’ve modified it a bit over the years, replacing some of the ketchup with a can of tomato sauce to make them less sweet.
Oh, geez, that’s what immediately jumped into my head… 