If the highfalutin James Beard Foundation were to bestow Mr. Beef, the humble River North street food stand, with an award — say, naming it one of America’s Classics — Chris Zucchero says he wouldn’t accept the prize. In general, fine dining ticks Zucchero off, from the brigade system in the kitchen to the paltry portions of a tasting menu.

Still, Zucchero says his father, Joe — who died on March 1 — would have scolded his son, telling him to shut up and graciously take the medallion if the Beard Foundation came calling. Zucchero likens Mr. Beef to a punk rock band, disrupting a music industry full of saccharin pop stars. He specifically compared the stand to Fugazi, the D.C. outfit that marched to its own beat in the ’80s and ’90s, putting out albums on upstart Dischord Records with hits like “Waiting Room” and “Give Me the Cure.”