I would suspect that solid surface or engineered stone sinks would provide the flattest surface that would rest against the underside of the countertop and thus minimize the gap. See sample installation instructions.

Hi, I did the same thing in my last kitchen, i.e. an undermounted apron front fireclay sink (Shaw) and a stone countertop, and it worked totally fine. I am germaphobe and am religious about washing out the sink so a "dirt groove" would be deeply uncomfortable to me, too. In our case, that gap was caulked well (I used white so it sort of blended). I don't know if my installer did something incorrect when he caulked that gap, because your example photo above shows it uncaulked, but I am glad he did. If you do the same I don't think your wife will be unhappy with the "dirt groove" and she'll get the look she likes. Good luck!

If getting a perfectly smooth interior surface is not possible, i think we will have to do something like katrinavhh shows in her photo. At least with this option the square corners of the quartz top touch the top flat of the sink vs. the rounded part like in my photo. This, when caulked, should give a nice tight seam/corner.

Matt: Give me a call, please. 248-842-5693

In my case the stone slightly overhangs the sink - which I think is a negative reveal and Joe says that he likes that the least. I do have silicone caulk between sink and stone. I've had my sink two years and forget about the area under the counter. This post prompted me to check it. No gunk on the entire left side and most of the back. A small amount, which I easily removed with a wet paper towel on the right side. My drain is on the right, so I use that side of the sink more. Like many parts of the kitchen, cleaning maintenance is needed, but it is not a big deal. My previous drop in sink with caulk on the exterior edge between sink and counter was a much bigger maintenance issue. My sink is a Kohler Whitehaven.