Normally it is finished just like an other drywalled corner, with a corner bead.

Darn. I was hoping for something other than drywall.

do a wainscot/board and batten under it

you could do any type of wood trim accent. you still may have a small lip, but not as much.

basically something like this

but it would be on the top

or you could use thicker tongue and groove to build it out

or, just top the ledge w/some nice wood. (I'd use walnut)

or paint and line it w/photos

can you step it down?

inset what's underneath the ledge??

Great ideas. Thank you. I love the wood trim options or the shiplap.