Lightly oil a 6-by-10-inch pan (approximately 3 cups).
Bring the water to a boil in a large saucepan.
Slowly whisk in the polenta.
Cover and cook over low heat, whisking often, until thickened, about 10 minutes.
Stir in the olive oil and cheese, season with salt and pepper.
While hot, pour into the dish.
Let stand until room temperature and firm, about 30 minutes.
Cover with plastic wrap and refrigerate overnight.
Cut the polenta into 1-inch-thick slices.
In a large non-stick skillet, pour in olive oil.
Fry the polenta slices over moderate heat until golden brown and crisp, about 8 minutes per side.