showing iphone on external monitor, but MONITOR in portrait orientation?

I'm trying to display my iPhone on an external display monitor. Works great using a digital lightning adapter.

BUT - I want to turn the monitor to portrait orientation so my phone and the screen are in the same orientation, tall and skinny, like a movie poster. The normal iPhone display on an external monitor is a little vertical (portrait) iPhone screen in the middle of a wide screen of unused space.

The monitor I am using does not have a native portrait orientation setting. (they don't normally)

I can do this with a laptop or computer - I go to the display settings and tell the output to be portrait. That works fine when I have a computer driving the monitor.

But I want to do this directly from my iPhone. Is there a way to change the monitor output settings on my iPhone? Is there a setting that can tell the monitor to display in portrait, the way the computer can tell it to do that?