With a large hand sanding block with a sheet of 80 grit. Because this is flat, I'll likely use a 6" RO sander, carefully, with 120 or so to flatten the surface a bit more. Then varnish.

Your drop boards are solid(I assume) so you could do the same. The biggest mistake I see made to brightwork is too much incorrect sanding; coarse grit paper hand held, various sanding machines used like grinder. This is what dips and cups the surface. Think flat.