Possible Clues:

• eg Medusa
• Ferocious woman taking more than half the cheese
• Petrifying monster
• Either Stheno, Euryale or Medusa
• In Greek myth, a snake-haired woman whose look turned men to stone
• Similarly restricted, ex-VP left formidable woman
• Ugly sister refused a drink on her return
• In Greek myth, a snake-haired woman whose look turned watcher to stone
• Italian cheese
• Monster with no drink to knock back?