Build higher toe kicks. The standard is +/-4" and you could make taller ones or build a base the same dimensions as the toe kick length and width and set the entire thing on it, and trim it out with baseboard.

You could even raise it up with a couple pieces of 2x4 and cover the gap with baseboard

You could also get thicker countertops (I've seen some quartz counters that are 4" thick). Go to houzz.com and type in +counter +thick to see pictures.

At my last house we did some updating including new granite counter tops and undermount sinks in all 4 bathrooms. We put a piece of 1 x 3 oak on top of the oak vanity frame and simply placed the granite on top of that. I had stained and or painted the vanities also and with the additional piece of wood painted the same color it was not noticeable. This increased the height by 3 inches and with the 1 1/2 inch granite a total of 4 1/2" higher. It really did look great and not at all noticeable unless I guess you are a paying close attention to under the counter space.

Thanks for the suggestions. This is my next project after Christmas. :)