I cut the walnut to 5mm thick at the table saw. You could use a band saw or even cut by hand if you wanted to.

For the holder I needed to 2 pieces of walnut (front & back). To make them the same thickness I used a technique I demonstrate here:

I wanted some contrast for the sides so I cut some 5mm thick Padauk to create a border around the passport.

Those pieces got glued into place and when they were dry I cut off the excess walnut with the band saw.