One of my early benches had this drawer unit in it.
When I built a new bench it ended up a few places in the shop, most recently over by one of the vacs.
It was full of all kinds of things.
I took the drawers out and added some wheels.
This must've been about when I settled on how I make utility drawers because I still make them like this .
I had some white oak left over from a China Hutch I made someone years ago. I rip it into some usable parts.
Some of it becomes a frame for the new top that I Domino at the corners. I rabbet the short pieces and stop rabbet the long pieces. Then I chop out the corners to make them square.
Here's a great use of your bull nose plane.
I glue in the top which is MDF like the drawer unit itself.