Perhaps I'm missing something really obvious, but I've done a little searching (with monitor not being the ideal search term for Kdenlive), and I have skimmed the manual. I can't seem to find a way to use two physical screens with Kdenlive.

To be clear, I edit using laptop with an external monitor attached. Ideally I would like to be able to throw the clip/project monitor on the external screen (actually vice versa, but that's slightly beside the point).

Is this possible? If so, what am I missing?

What happens when you select Monitor -> Switch monitor fullscreen ?

Aha. I see two different behaviours from that. If I have the GUI on my primary screen, then the clip monitor is full-screened entirely replacing and obscuring the GUI. If I have the interface on my secondary monitor, and do the same, then the clip monitor is full screen on my primary screen leaving the interface on my secondary screen. The later being the exact behaviour I am looking for. So that's good enough for me. Thanks!

I don't use the 'Monitor -> Switch monitor fullscreen' method.

It's actually very simple to place the project monitor on your second screen - just grab the project monitor (hold down left mouse button on the word "project" below the project monitor box) and drag it to the other screen.