Being sick has given me time to curl up and pour over John Bengston’s Silent Traces-- a wonderful book on Los Angeles locations used in Charlie Chaplin movies. He points out that Modern Times (1936) used the Broadway Hollywood building—or at least a picture of it. When Charlie and Paulette Goddard are loaded into a paddy wagon, the background looking out the back door shows the the big vertical "Broadway Hollywood" sign of the building at Hollywood and Vine.
Coincidentally, The Los Angeles Times Sunday feature ”L.A.Then and Now” on May 4 focused on that intersection, mentioning the Taft Building, built in 1923. The Taft is across Vine from the Broadway Hollywood, which was put up in 1928 as the Dyas Company Department Store (Broadway took over the lease shortly thereafter). Read a history of it at NavigateLA, , which is where I found this picture that shows the big sign as it was in Modern Times.
Both buildings are being converted to lofts, right? The plan for the Taft was always to keep it intact, with the W Hotel wrapping around it. For the Broadway Hollywood you can check out the floor plans and rendering of the exterior here.