I could
swear the verb شلبط
shalbaT meant "to mix up; to scramble" in Levantine, which could make شلباطو a derivative of it -- compare the general-Arab dish مخلوطة
makhluuTa lit. "mixed up", from خلط "to mix".
However, I can't find that meaning anywhere online. The only thing close (after searching for شلبط، تشلبط، متشلبط, all of them possible derivatives) was these two second-page Google results for مشلبط:
على طول من نخعة في راسي وقعت مشلبط بالرديف فعال المجنون هههههههههه
اوكي بس ما تظلمو عشان التجربه حتكون قاسيه حيكون وشو مشلبط زي ما انت شايف
(I don't 100% get the first one, but the second is "Okay, but don't victimize him, because this try's going to be rough -- his face is going to get all
[mshalbaT] as you can see")
...so, given the dearth of confirmations, that doesn't seem plausible. Its common meaning instead seems to be "to be stuck on [a person/lover]", but I was also able to find (1) a page defining it as "to mutter" and (2) a Tweet defining تشلبط as "to climb"... I can't really see a link to food in any of those.
Can anyone suss something out, or would شلبط just be a red herring?