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.