Put the milk, butter and a pinch of salt into a saucepan. Heat the milk until almost boiling, then turn the heat down and pour in the polenta in a slow, steady stream while stirring continuously with a wooden spoon. Keep stirring for 5 minutes until it thickens. Spoon into a 20 × 30 cm tray lined with baking paper. Smooth the top with a spatula. Allow to cool completely, then cut into slices.
Heat a grill until it is very hot. Brush the eggplant slices on both sides using 1 tablespoon of the oil and lay, side by side, on a baking tray. Add the capsicums, skin-side up, and the shallots, skin-side down. Grill for 15 minutes, turning the eggplants over halfway through, until the capsicum and shallot skins are blackened all over. Set aside until cool enough to handle.
Arrange the chilli, cut-side down, unpeeled garlic and polenta slices on the baking tray. Brush the polenta on both sides with 1 tablespoon of the oil. Grill for about 6 minutes, then remove the chilli and garlic and turn the polenta over. Grill for a further 6–8 minutes until the polenta is golden brown.
Scrape the flesh from the chilli and garlic, mash and mix with the remaining oil and the lemon juice in a small bowl. Peel the skins from the capsicums and slice the flesh. Peel the shallots. Arrange the polenta slices around a wide platter. Pile the capsicums, shallots, eggplants and olives in the centre and spoon over the chilli dressing. Top with parmesan and basil.