Use a jig saw blade made for cutting counter tops. the blade will cut on the down stroke rather than the up stroke. This makes a nice smooth cut.
I always cut on the pretty side, but I lay down a strip of 1 inch masking tape and make the cutting line on this tape and then cut the tape. This just makes sure the cut is not a jagged broken chipped cut.
Anyway, its a counter top saw blade, cutting on the down stroke, you can see the teeth are going a different direction than the others.
Then lightly sand the cut or go over it with a ball bearing counter top router bit. This is optional. Sanding will make it nice, Then you add your glued on strip to hid the cut if its exposed.
If the cut will go up the rounded attached splash board, you will need a longer blade and much caution is needed in the corner cut. If the blade jumps out of the slot the top will be damaged. when you get to this area and are very concerned, use a hax saw with a sharp blade.