What to use for huge exterior window gaps?
I'd be tempted to try and get a piece of wood in there! Cut a piece over length and leave it out in the rain leaning against a wall etc. Wet wood will eventually bend (or you can encourage it over a couple of blocks by adding a bag of sand etc.) and get something the approximate curvature you're looking for and then cut it to length.

Not the quickest solution, but cement will crack up eventually as the window moves about through the seasons.

If it's too thick to bend naturally, (it looks to be on the upper limit at around 3/4 inch or so) you could laminate a piece up. Run some timber through a table saw to get 2 or 3mm thick strips and then glue them up over a former the same radius as the window. Again, not quick but oh, so pretty!