Add the chicken broth to a pot and bring it to a boil.
Once boiling, turn the heat down to a simmer and slowly add the polenta whilst stirring, until all the polenta is combined with the stock. The consistency here will be wet.
Next, add the butter, Parmesan, and chopped rosemary to the mixture. Stir until the butter has melted and the polenta has thickened up a bit, around 5 minutes.
Pour the cooked polenta into a lined baking dish or baking tin (10x8-inch) and spread it out evenly. Let the polenta cool completely then chill in the fridge, covered with plastic wrap, for 3 hours or overnight.
When you're ready to bake the polenta fries, preheat the oven to 400F.
Once chilled and completely set, remove the polenta from the tray and cut it into rectangular fries. You can cut them thicker or thinner depending on personal preference.
Place the fries on a lined baking tray and brush with olive oil. Bake in the oven for 35 minutes until golden brown and crispy.