Welcome. Don't have a recipe, but a place that sold the mini burgers, was called White Castle. You can buy them by the case (if you don't want to spend lots of time on the burger appetizers). I bought them in smaller packages at the market for the holiday weekend, or whenever I want a little bite. Aunt Dot makes a good point. You might be able to find these too, at a food warehouse store. You can take a look-see here. The sides/slyders/sammiches look good also.
Another idea...get a large crusty loaf of French bread or focaccia, & cut it down to size.