White Castle burgers are also known as sliders, an apt description of how they behave in your GI tract.
You can get them in your grocer's freezer nowadays. Amazingly enough, the freezing process does absolutely nothing to their stomach-twisting properties. Why this is so is left as an exercise for the reader.
In my neck of Maryland, the closest thing we have, or had, was Little Tavern. Same burgers, different name, and now there's only one left as far as I know, in my town of Laurel.