It's a single-hole unit by Kohler. The problem is that the nut that screws in from under the sink to secure the faucet is round (2-1/4 inches diameter), not six-sided. So there is nothing for a pair of vise-grips or a channel-lock wrench to grab onto even though the nut is rather thick, maybe 1/8".
It has two threaded holes for screws that dig into the bottom of the counter to keep the nut from loosening. I've loosened the screws, and tried using them to get leverage to loosen the nut. No luck.
I don't know if a basin wrench will work on a round nut.
I sprayed with a lubricant, but the real problem is that I can't get a good grip on the nut.
Eleven years ago, most likely I installed the faucet onto the new sink before I placed the sink into the counter cutout, so everything was more accessible. I'm trying to avoid removing the sink, but that's my last resort if nobody has some other suggestions.
Kohler sucks, for using a round nut. If they hadn't used cheap plastic, the handle wouldn't have broken and I wouldn't be going through this ordeal. On the other hand, I've used it for 11 years, and it was in used by the previous owner for an unknown number of years. He and I are both single, so the faucet doesn't get the heavy use that it would with a family of, say, four.
TIA.