You may already have this fixed, but you can rent a puller to remove a pulley. Mostly on that stuff, these days, the replacement is sold as an assembly with the bracket already attached. You get a pulley assembly, not just a pulley. That makes it much, much easier to fix and you don't need any special equipment to remove it. I'd recommend getting the replacement part before tearing it all apart so you know what exactly needs to be removed.

Jim
Edit: on closer inspection, it looks to me like the bearing seized on the pulley shaft, which is why there is so much buildup of belt material around that pulley (the pulley stopped turning smoothly and the belt slipped on it). That led to overheating and eventually the pulley broke. You may want to see how smoothly the remains of that pulley spins and make sure you don't need to replace the whole assembly the pulley drives (due to a bad bearing). That assembly looks like the motor...