The surviving restaurants have holes in the counters, as if they had open fires, or fished the cooked items off coals inside the structure. Might have been bowls.
Here’s an indoor restaurant from ancient Ostia, the menu (like fast food places today) of their most popular products is made into a mosaic on the wall above the counter. People might not be able to read, so the pictures made it easy enough, they’d pay, they’d get their food. Nice shot of it here:
https://upload.wikimedia.org/wikipedia/commons/1/1e/Ostia_antica-13.jpg
Thanks again, fascinating stuff, a society frozen in time.