These are the "travelling box" reproductions. They had two in progress.

Inside are lots of compartments and dividers, joined to the sides of the box with stopped dadoes.

You start by scribing both edges of the dado with a marking gauge, before using a chisel bevel-down to begin digging out the waste. Be most careful at the entrance of the cut, where you don't have walls to guide you. There actually two slightly offset dadoes here, almost in line but not quite.

Then you scribe both walls again, to deepen them. You really need two marking gauges, so you don't have to change their settings. And they need knife-style cutters in them, to create a smooth dado wall.

Then you just chisel out more waste, getting close to final depth. Every once in a while you go to the end of the dado, using the chisel vertically to chop the end clean and square.

Last, Headley stuck his chisel in a simple wood block, turning it into a router plane to finish off the bottom of the dado!

Don't have a router plane? Just make one! This highly effective yet simple jig is nothing more than a narrow chisel stuck into an offcut from another job. 

The chisel is held in with a wedge. Headley said to be careful when cutting the slot for the chisel and fitting the wedge, or the chisel won't hold its setting. The chisel is tilted backward at a slight angle for better cutting action.