Probably pretty hard without a router, there might be a clever way to do it with other tools I can't think of.

Maybe look into using some keyhole brackets? You'll need Forstner bits and probably some chisels.

Could drill two shallow recesses at each end with a Forstner bit and chisel out the straight edges:

https://www.amazon.com/Single-Keyhole-Hangers-Hanging-Fasteners/dp/B0916NX7B8/

Or just go with round ones and drill two recesses: one large for the bracket and one smaller for the screw head:

https://www.amazon.com/Adiyer-Mortise-Keyhole-Hangers-Brackets/dp/B08TTRNNFJ/