A Perfectly Runny Egg and Sage Sausage Complete This LES Sandwich

No edible item is more New Yorky than the breakfast sandwich, made with egg, American cheese, and bacon, sausage, or boiled ham on a kaiser roll — available at nearly every deli and bodega. But this cherished sandwich has been modified by time and contemporary preferences, and now variations can be found, or created. Appearing every Wednesday for the rest of summer and into the fall, this breakfast sandwich hack column will ferret out those wayward modifications.

Most breakfast sandwiches based on the classic prototype of egg, cheese, and meat are intentionally easy to maneuver, allowing you to, say, read your morning paper or pretend to work at your desk while holding a sandwich in the other hand and eating it. Not so with the spectacular egg sandwich at the Lower East Side’s Factory Tamal, which serves a lot more besides tamales.

The egg sandwich there comes in several permutations. If you just want egg on a brioche with special orange sauce, the charge is $3. Add the wonderful sage sausage link, and it’s a dollar more. Pile on sliced tomato and a shaving of gruyere, and the tariff rises to $5. It’s this last version I recommend. But why can’t you eat the thing with one hand while doing something else? Well, the egg is cooked over easy, which means if you don’t eat it with both hands and very carefully, it will squirt all over your pants and shirt, which will cause your co-workers to point and laugh as you run for the bathroom to sponge off. Nevertheless, this sandwich is well worth the humiliation. 34 Ludlow St., between Grand and Hester streets, Lower East Side