The culprit here is a Kohler kitchen faucet with a single handle control and a pull out spray head from the spout. It's a model which we bought at Home Depot's Expo spin off before they closed.
The problem with it, was a slow drip from the bonnet which eventually stopped after each use. I called Kohler's customer service line and they diagnosed the problem as the shut off valve. They sent the necessary valve free of charge with an expoded view to assist in the installation.
I rebuilt the faucet with the new valve and the same problem persisted. A new call to Kohler, Wisconsin and I explained the situation. New diagnosis, its the check valve. They send along another bag of plastic and brass hardware. Again, gratis. It seems this model had a checkered history with this problem and the engineers at Kohler have developed a fix for it.
At this point you must do something counter-intuitive. You must remove
3 or 4 parts from the machined body of the faucet and replace them all with one new brass plug. This changes the internal hydraulics but it seems to be effective as the dripping has ceased.The lesson learned here is that we like single handle controls (temperature modulation and off & on) and that leads to complex internals which eventually need replacement. There is no free lunch.
Kohler's people spent a lot of phone time with me and provided all the required parts free.
Joe G