There’s a little corner of sandwich heaven hiding in plain sight in Lisle, Illinois, where Schmaltz Delicatessen has been quietly perfecting the art of the Reuben while flashier eateries come and go.

Nestled in a Las Vegas shopping center far from the neon-drenched Strip sits The Bagel Cafe, an unassuming eatery where the Reuben sandwich has achieved legendary status among locals who guard this ...