You can tell looking at the direction of the grain in the cut that this was a super weak part of the wood so it was bound to break.
I picked an old steel kick plate and cut a piece off of it.
With the dremel we carved a groove to house the steel reinforcement,
On the other side, because of the geometry, we could just use a regular screw, but making the hole had to be done carefully so we drilled first a smaller pilot hole and then used a larger drill bit,
We used epoxy to join the pieces,
Then let it cure, clamping things to make sure the legs didn't touch each other,
Once cured we ground off the metal to contour to the wood, sanded it, and applied a coat of danish oil.