Line a 24cm square tin with baking paper. Oil a large baking tray.
Put the milk and chopped rosemary in a saucepan set over a medium heat and bring to a simmer. Whisk in 250g polenta, the parmesan and butter, then season generously. Tip into the tin and level the surface with a palette knife. Transfer to the fridge to chill for 1 hour.
Preheat the oven to 200°C, gas mark 6. Turn the polenta out onto a board and cut into 2cm-thick soldiers, each 7cm long. Arrange on the oiled baking tray, drizzle with the 3 tbsp olive oil and turn to coat.
Sprinkle with the remaining polenta and turn again to coat. Bake the soldiers for 30-35 minutes, turning every 10 minutes, until golden and crisp. Season and serve with the boiled eggs.