DIAGNOSIS Coffee oils and fine grounds have baked onto the basket rim and the showerhead gasket, acting like glue.
FIX Run a clean cycle with a cleaning tablet. While the machine is still warm but unplugged, grip the basket handle firmly and twist counterclockwise while pulling down. Do not rock it side-to-side.
IF THAT DIDN'T WORK Remove the upper showerhead assembly by unscrewing the center bolt. This gives you direct access to push the basket out from the top. Clean the silicone gasket on the showerhead thoroughly.
HEADS UP Forcing the basket can bend the precision tabs on the basket or crack the plastic brew head. Always twist, do not pry.