My family had one from decades ago that's falling apart, so I made a replacement. I went with toothpicks as little dowels to help join the crossbars to their supports, since the flat glue joint didn't hold for all of them.
I had this one on my list for a while, but also recently found a video from 3x3 Custom doing the same project.
Thanks for the photo! I now realize that the top sits on the pieces that run perpendicular to them and it all comes out as one piece. For some reason I was thinking that they fit onto a lip or something on the box side.
Clearly, I've never seen this style cutting board before lol.