As separate pieces, you could rig a slight tilt angle on a sled to go thru a planer and slowly work your way thru the material depth.
If they are already glued up, bandsaw would be my choice.
If I were any good with a hand plane-i would say that too
Wife wanted more counter space...so i scrounged what i had left of walnut and maple and made this. coffeeshelf1.jpg I wasnt happy with the kitchen counter being thicker and the fact that I could see the bracket underneath so i did a little more adjusting to hide those things from view and ended here...
Unfortunately, you will not be able to get to "dust free" in a woodshop environment. If you choose to go down the dust collection/filtering route, know that these things will reduce dust but not eliminate it entirely. I would think awhile about if this is acceptable for your other hobbies....
Alright-now I'm getting close to done I think. Decided on double bevel on cover with single bevel on base. Interior base image also done. Cross is dowel mounted thru top and because I screwed up the holes, I hid them with some walnut "dimes" on the inside. The top/base used a light pecan s...