There are a couple of ways.

First way is to clean up the flat edge, get some wood, poplar would be great, glue on the piece of wood and clamp it overnight. Remove the clamps and carve the shape to match. Mark the front with a vertical reference ("0") line and work back from there. Sand to smooth and repaint.

The second way is similar. Clean up the flats, insert a screw and let the head stick out 1/4" or so. Apply some epoxy putty such as "Quik Wood." While it's still plastic, rough shape a little oversize with a putty knife or old credit card lubricated with water and Dawn. Let it set up then carve, rasp, and sand to shape. Paint it to match.

which of the 2 options would be best (most fail proof) for someone with patience and a steady hand, but not great woodworking tools? Is the quick wood material basically like building up the missing area with a putty to resemble the shape of the wood that was there? and will it hold up like a real piece of wood would?

Good question. I had to think about it.

I think the advantage with the epoxy is that if you don't get it right the first time, you could add some more easily and start over.

Just go slow and keep a good eye on "round".

BTW, you can get QuickWood at hardware stores and places like Lowe's

Here is a link that might be useful: Quickwood