[Aliantha]

A round of sandwiches is just one sandwich. A round of toast is just one slice of toast, unless you're going to make two slices of toast into a sandwich I guess.

My mum used to use that phrase quite often, and that was always the context.

If there were a few kids over and Mum was making sandwiches for us, she'd say, "I'll just make a few rounds of sandwiches.", meaning more than one sandwich.

I don't know for a fact, but I suspect the term is quite old and from the days prior to bread tins when most loaves were rounder rather than square.