Help Fixing a Dripping Sink

[benjamin_diy]

My bathroom sink is leaking/dripping at the spout. When I turn off the water line to the hot water, the dripping stops, so I assume that this is the handle that I need to replace the cartridge/seat and springs. My main problem is that I cannot figure out how to get to the cartridge. I unscrew the set screw, and then the part directly beneath the set screw appears to unscrew, but then nothing seems to come up to reveal anything. When I unscrew that part, it just loosens the whole handle fixture and just shifts around in the hole in the granite/marble. If anyone has any idea on how to get to the cartridge to replace it, I would really appreciate it. I am attaching photos of my faucet so that you can see what it looks like.

Thanks,
Ben