Boil water in a large saucepan. Gradually add polenta, stirring constantly with a whisk. Add the milk. Cook, stirring constantly, until mixture thickens and boils, around 10 minutes.
Turn the heat off, stir in Parmesan and season with oil, salt and pepper. Spread polenta evenly onto a 8½×12-inch baking sheet. Press plastic wrap onto surface; chill in the fridge at least 1 hour.
Preheat oven to 400°.
Uncover polenta and cut into 4×¼-inch strips. Sprinkle some parmesan and separate fries. Arrange on a greased baking sheet (I used oil).
Bake fries around 25–30 minutes. Let them cool for at least 15 minutes before serving them along with your favorite dip.