Bring the water to a boil in a heavy saucepan and add the salt. Slowly add the corn meal while whisking constantly. Continue to whisk until the mixture thickens, about 2 minutes, then switch to a wooden spoon (or rubber spatula). Let simmer over medium heat, while frequently stirring, until the funchi pulls away from the sides of the pan, 20-25 minutes. Stir in the parmesan, rosemary and butter. Season to taste with salt and pepper.
Spread the funchi out on the baking sheet into a 1cm/0.5″-thick layer. Smooth the top with the back of a spoon or rubber spatula. Let cool slightly, then cover and refridgerate until cold and set, at least 30 minutes.
Heat the oil to 375F/180C. Cut the polenta into fries and dust them with flour to prevent them from sticking. Add the fries to the hot oil and fry for 4-5 minutes or until golden. Transfer to paper towels to drain.
Just before serving, fry the fries a second time for 1-2 minutes or until crisp. Transfer to paper towels to drain. Serve immediately.
You can (carefully!) crisp some fresh rosemary in the hot oil and sprinkle it over the fries