Am finishing my basement - have had it water-proofed, put a vapor
barrier on the walls, will insulate, etc. The problem I'm running
into is in the framing.

I have a ledge that runs around most of my basement (knee-wall/frost
wall??). It's 3 feet up and 23" wide.

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How do I frame this? Some ideas I've had involve a single top/bottom
plate with the 2X's cut at 45-degree angles - or joined at 90-degree
angles. I really don't want to have two top/bottom plates unless I
absolutely have to.

Is this an old house with the basement added? In Michigan it's called a
"Michigan Basement." The footings are below the outer wall down 3 or 5
feet below grade depending how far north you are.

Yeah, exactly. Maryland though.

I'd use a 2x6 as the bottom plate of the upper wall and construct the lower
wall so that its top plate is level with the top of the 2x6. Then run 3/4" x
24" plywood between the walls as a shelf. It will give you storage
space --- maybe too much storage space : )

I can't envision how a 45 degree wall could be made to look attractive but
I'm not really good at envisioning : (