Bring water and stock to boil in large, heavy pan. Add salt and reduce heat. Add cornmeal gradually, whisking constantly. Cook, stirring constantly, about 10-15 minutes. Add oil and parsely, then grated cheese.
Pour cornmeal mixture into a wetted half sheet pan. Set aside to cool until surface is dry. Transfer polenta, upside down, onto another baking sheet. Cut polenta into circles with decorative cutter about 3 1/2 to 4 inch in diameter.