A prying tool could help. It needs to be arranged so that the force pulls straight up, along the axis of the valve stem. The nail-pulling claw of a hammer or a crow bar is a common prying tool, but we'll need to add a little more to the equation to make it work.
A block of wood laid on the porcelain might be about the same height as the top of the valve stem and will give a place where the hammer can be rested for maximum leverage and minimal marring of the porcelain. A screw inserted into the valve stem can provide something for the hammer to pull against. You might have to buy a screw the same size but longer length as the one that holds the handle so that the screw can be wound fully into the stem while still being tall enough for the hammer to engage. It might also be necessary to add a washer under the screw's head if the screw is prone to slipping through the hammer claw.