I don't recognize it, but do agree it is not Broadway. For starters, most Broadway was polished brass, and mostly lever handles. Their designs were mostly a little fancier than what you show. That's good , because Broadway is out of business, and very little parts support is available. Ingersol Rand is hoarding the last available parts and will provide them under warranty to the original purchaser with receipt!
Remove the handle, take off the flange , and unscrew that diverter stem. post a picture of it. Someone will probably recognize it/