Fill the offending cup with hot, soapy water. Let it set over night, then use a Brillo pad and gently rub it clean. If you don't have a Brillo pad (good heavens! ) then spray it a little oven cleaner and follow the instructions.
"Food is our common ground, a universal experience." - James Beard
I seem to remember Mama suggesting ammonia for stove grates. Something about a plastic bag with ammonia in it and sealed tightly around the parts you want to clean. I don't remember the details though, if the ammonia was cut with water or not... I hear it works great, no scrubbing needed.
__________________ Give us this day our daily bacon.