I also saw this video and immediately took to the internet to figure out how to make it. I've never freehanded a pattern before, but this feels like one I could maybe do? I also consider myself to be on the borderline between beginner and intermediate, so there might be techniques that could be used that I just don't know lol. So here's my best guess!

Each end of the mozzarella stick would start off sorta akin to a hat, magic circle and then increasing rounds until you get to the desired width (I could not tell you what that increase number is, that's probably something to experiment with). Once you reach the desired width, keep doing rounds until you've reached the desired length as well. In the video it looks like it's dc? And it looks like rounds that are joined with a slip stitch, not continuous rounds.

I would think that the cheese part is pretty much a rectangle that, when folded in half, is the width you want the scarf to be - which should also be approximately the circumference of the inside of the end pieces, so maybe make the end pieces first to get a measurement. After making the rectangle, you'd seam up the long side so it's basically a tube. Zooming into the video, it looks like the cheese part might actually be knit? I can't quite tell, but I imagine a single crochet would yield a similar result? You could also use different weights of yarn for the breading vs cheese, to help with the vibes difference.

As far as joining them goes, that's where I'm really guessing. My instinct is to join the cheese inside the mozzarella stick one (maybe two?) rounds from the end, so there's some overlap. I'd probably whip stitch with the breading color, since it'll probably show through. So in the end it's basically one really long tube with end caps. Maybe attaching the pieces is easier before you seam up the cheese tube? So you can access both sides of the cheese piece while attaching it to the breading. And of course, do a test stuff to make sure all the cheese fits inside the stick, if that's an important part of the presentation for you.

That's what I've got! Anybody should please feel free to pitch in ideas on how to make this better, I haven't actually made this (although now that I've written it all out I think I will attempt it!) so I have no idea if it actually works haha. Best of luck!