A sturdy (made for freewheels, not for cassettes) chain whip too is the best way to remove such a stuck cog, seeing that it appears to be well-attached to the wooden block.
It can take a lot of torque to remove these threaded-on cogs!

I've also used really big Channel-Lock pliers, gripping using the jaw tips between teeth or (since your cog is already toast) perhaps grasping the cog using the higher-leveraged inner faces of the jaws(??). Use caution to prevent injury!
Gripping tightly with big-handled pliers will slightly ovalise the assembly elastically, which should further assist with the surfaces breaking free of one another.
Compressing the smallest cog a few times first (from different "clock" angles) using the vise jaws will help loosen it (the teeth already being broken...).

Heating briefly with a torch almost always helps reduce frozen parts grip on one another. Some of the more-inward cog spacers are plastic however, so don't apply heat for too long.