This involves a wood holder, so relax.
On a number of occasions, I made coasters of either slate or marble, complete with a ground in recess for the drink and a cork backing. Over the years, I'd guess I made around 500-600 of them in batches of different sizes, mostly to give away in sets. The majority of the sets were 8 coasters, wrapped with a tape, and handed out to house guests, at Christmas, to friends of the kids or relatives.
They always began as slate or marble 12" tiles, which I cut on my diamond wet saw to 3-7/8" squares. Cut, rinsed and left to dry, I could proceed at my leisure, using jigs I'd built and improved upon over the years.
The first step was to grind in the recess. Since the tiles were about 1/4" thick- regardless of material- I kept the recess to around 1/16". It was mostly for looks. The grinder was fashioned from a 2" thick block of cherry, which I drilled and fitted with a
3/8" carriage bolt, recessed, that permitted me to chuck it in the drill press. Since the head was recessed, the hole was filled in with Bondo filler and the face sanded smooth. The abrasive was 40 grit floor sanding paper, which was epoxied on using 10 minute epoxy. Since the epoxy softens with heat, it was necessary (thanks to a fellow here in rww long ago) to temper it through use and letting it cool. The first time it was used, it'd begin to soften after the second coaster. I'd then let it air cool and go at it again. The second time might take 2-3 coasters before it'd again soften. This was repeated until the stuff never softened- about 5-8 go-rounds.A jig held the coasters square and aligned under the drill press. In addition, there were holes and a "wall" all around the coaster so that my shop vac could collect the dust. It worked swell. I'd press the turning disk and abrasive against the coaster, let it grind for about 20 seconds, then back off to clear any trapped dust. Each coaster took about 3 of these cycles to develop the circular, ground-in, depression from the grinder.
Using a sheet of 1/8" automotive cork, I laid it out on my workbench and applied contact cement. Each coaster also got a coat of contact cement on its back, and was then applied to the cork sheet and weighed down. When dry, I cut each coaster free from the sheet.
The final step was trimming the cork and beveling the edges of the coasters- top and bottom. This was done with a jig on my table sander. The jig had a Formica base and was just as wide as a coaster. The base was at a 45 degree angle to the belt, and there was a stop that could be adjusted to limit the "forward" motion of the coaster, giving a uniform depth of the bevel. The belt was just a 120grit that had gotten a bit old. Surprisingly, a belt would do 100-150 coasters at a time. The beveled bottoms, including the cork really looked professional and the overall look and feel of the slate or marble coasters was terrific.
Next: making the holder for the coasters.