1 Start by making the polenta: in a medium pan, bring the milk and 675ml water to a boil over a medium-high heat. Add the salt and olive oil, then reduce the heat to low. Add the polenta and simmer, stirring, for 5-10 minutes, until cooked – it should be thick, tender, and just pourable. Stir in the butter and parmesan. Pour into a greased baking tray and set aside to cool; cover and chill.
2 Remove the polenta gently from the baking tray and cut into 6cm x 1.5cm x 1.5cm chunks (like a chunky French fry). Gently roll each one in the 20g parmesan. Place the polenta frites on a parchment-lined baking sheet and chill until needed.
3 To cook, heat the vegetable oil in a deep fat fryer, or heavy pan, to 180˚C. Fry the frites, in batches, until crisp and golden – 3-4 minutes per batch. Drain on kitchen paper and while still hot, season with sea salt and the rosemary. Serve immediately.