HTC has always followed the MHL standard, this is what you want -
For only $8.84 each when QTY 50+ purchased - Micro USB to HDMI® MHL Adapter - Black
Don't sweat the 1080p bit on your phone - that's been reported working fine with the Droid DNA 1080p screen.
edit - Plus the HDMI cable as marctronixx said (on the ninja!
). Monoprice sells those for less too, very high quality.
Always power your MHL adapter.