Try using a slurry of Bar Keepers Friend on a soft cloth.

Usually, I just wipe mine down with a slightly damp paper towel unless I've spilled raw meat or eggs or something in which case I use a little Clorox Anywhere. I always make sure to go over it with a dry towel after cleaning it. My finish is pure tung oil, which seems to be quite the work horse. The other night, I marinated some chicken with the dark thick soy sauce in the marinade and accidentally splashed a few drops on the butcher block. I didn't notice until cleanup time after dinner and I just knew there would be a brown spot since it had been sitting for so long. Nope, nothing, nada - wiped right up with a damp paper towel. I've heard tung oil finishes are supposed to be redone every year or two, but it has been 5 months and nothing phases this countertop. It's my granite that I can't get the oil spots out of!

I'm with Jack, except I try not to peel any layers. I try to dig when the row is dry; so the bulbs come up pretty clean, and if there are any extra dirt clods, l remove them without taking any more skin than is absolutely necessary, once the bulbs have dried down. Then the dirt powders off and the bulbs have cured to a certain extent and are not likely to bruise. I don't grow for market or the fair; so I really don't care if the outside skin is pristine or not. IMO maximizing the skin layers makes for longer storage. It all gets peeled away completely when I crack the bulbs for cooking anyway.

Love chispa’s comment! So true! Similar to the conversation I was having with my BIL last week. He’s a medical director in a large hospital, bemoaning why, as flu season approaches, people entering won’t use the blasted hand foamers. I said it was because you are asking them to remove THEIR germs to help others. It is OTHER people’s germs we perceive as dangerous. So I said he should put out tubs of germ wipes instead, with a big sign that says, “Protect yourself during flu season! Wipe all knobs, chairs, and surfaces you touch!” He says compliance is going through the roof. LOL. Re cleaning, just to unhijack here, I clean mine every 6 months. But there’s never much dust, because, I’m guessing, we run HEPA cleaners 24/7 for my allergies to everything in the universe. Gonna try the newspaper thing, though, for sure.