I am looking to connect a phone via HDMI to a monitor/TV that is positioned in portrait mode (sideways). I have an app that runs in portrait and I want it to be displayed to take up the full screen. I believe this might be called exploded portrait mode, but I am not sure.

The issue:
When I connect a phone to the TV, I end up with the phone being displayed in portrait mode in the center of a landscape oriented TV. This means that there are large black bars on either side of the image, and the image is very small. Instead, I want the portrait image of the phone to appear on the TV sideways and on the full screen, so that way when rotated it will look ok.

Only semi-solution I have found
I have found the Galaxy Nexus (the original nexus, not the S2, S3, etc.) to do exactly this, but I am looking for some other phone which may behave the same way, since the Nexus is an older phone.