Studio Catering is rarely busy..as such the menu often changes. Indeed, I think the area was recently just closed for revamping -so whatever grilled gooies they had before may be soon gone. Nevertheless, the food there is oftenthe best QS choice in HS.
I can't find any specific info, and Disney doesn't post QS menus. It would appear it's open again, but as I said the menu often changes, so it may have changed. The 'grilled' item that had on the March menu was a grilled veggie sandwich. Studio catering is at the back of the park. It's between TSM and the Stunt Show, next to the HiStA playground. (A great place for the kids if part of your party wants to sit a little longer.)
I agree the dining choices in HS are limited.
Starring Rolls is good for pastry, but I'm not so keen on it for lunch. Also the set up is small, cramped and S-L-O-W. The number of tables is also seriously limited.
My other favorite is HS is Pizza Planet. The Pizza is not fantastic by any means (though it's better than it was 5 years ago). But the atmosphere is cute. If you can get an outdoor table and it's nice outside, then the outside activity is fun to watch.