I think you need to try Primanti Bros. restaurant in the Strip District. I think it's on 17th street. You can also visit them on Forbes in Oakland or on East Carson on the South Side. The Strip district is the original store. They began as a sandwich/breakfast shop for the wholesale yard employees that worked the night shift. They used to open at midnight and were open until noon, but eventually caught on with the late night drinking crowd and grew to be very popular. That's when I heard about it... As a native yinzer, I highly recommend them for their local fare.
Pittsburgh, PA