Sandwiches are the second-class citizens of the food world. They’re what you toss in a brown bag when you can’t eat a real meal. Those few, truly worthy sandwiches don’t go by the common name. They prefer to be addressed by a more proper title, like club, Reuben or po-boy.

When built with the right ingredients, though, the humble sandwich can rival the most intricately crafted dishes for taste. If you doubt it, head over to St. James Cheese Company, one of the best additions to the New Orl...