What you can use really depends on access, clearance, and what part of the cabinet and how much needs to be removed. Sometimes a sharp wood chisel and a mallet are the best bet. Sometimes power tools. Sectioning away small areas in a controlled manner is easiest with a precise tool like a fein multimaster. When you have more leeway a sawzall with a short blade can be equally effective...but a bit less precise. It's tough to offer advice without seeing it. I'm guessing that the vanity is installed in place, as is the countertop, and neither can be moved? If you do have to whack away at it with a hammer and chisel, be sure to not crack your countertop! A sharp chisel can make quick and easy work of things. A not-so-sharp chisel can cause nothing but aggravation. Mongo

If the undermount sink can be easily removed, this would give you better access to work. Be careful not to apply pressure upwards or downwards as this will crack the granite. With the sink removed you could get a wood chisle in behind the nut. Good Luck! Dan Martyn

@chiflipper, that kind of look like the Hansgrohe Metris that I'm going to use in my other bathroom: This is going to be a complete gut renovation so installing a wallmount faucet shouldn't be a big problem for the install. I'd hope that something like the Kohler Purist would come with the hardware necessary to install it properly (especially since the carrier and trim are sold separately). I'm looking at the wall mounts because the vanity is only 18" deep -- once the 13" hole is cut for the basin, there is only 2.5" of stone left on the front and back, and that's not enough stone to drill faucet holes :(

We have been happy with this Kohler Artifacts faucet at our prep sink. I recommend it if it fits your style. Our prep sink has an inside width of 28" and the reach is more than sufficient. There is a version that is a bit taller than this one. Plenty of height to place stockpot on top of cutting board for filling. Easier than lifting from bottom of sink. https://www.us.kohler.com/us/artifacts-single-hole-kitchen-sink-faucet-with-16-pull-down-spout-and-turned-lever-handle-docknetik-magnetic-docking-system-and-3-function-sprayhead-featuring-sweep-and-berrysoft-spray/productDetail/kitchen-sink-faucets/1062778.htm