OK, you are going to have a trench under the walk....keep it as narrow as you can. When you are done try and block off one end with a plank..on the low side. After the plank, backfill the trench to give it support. Then from the open end start filling and tamping with whatever fits. Ram it right against that board you put in. Pack it in...repeat until you get to the top. Then pull the board and backfill.

Simple.......put fillers on either side of the vanity and order a bigger top and cut it to fit between the walls. Or order a top made to fit.

All that gap is gonna look like crap! Dust bunnies forever.

Take a piece of wood the same thickness. Mark 2" on your line of cut on top of the board. Cut to the mark. Remove board, flip over and use a square to transfer the end of the kerf to the edge of the board. Do the same with the original 2" mark on top. The distance between the two lines is what you need to hold the top cut back by.

i.e. if the bottom kerf is 2 1/2" you would stop cutting 1/2" before the end. Then finish up with jig saw or whatever.

Try and unsweat it. That little neck'd down pipe might be a pita and have to be replaced.