Bring the stock to just simmering and add a couple of good pinches of salt. Add the polenta and stir in thoroughly.
Put on a very low light and cook for about 40 minutes stirring every five minutes or so. Add a little more stock or water if needed.
Meanwhile peel and finely chop the shallots. Soften without browning in the olive oil.
When the polenta is cooked, stir in the shallots and olive oil, along with a good handful of parmesan. Season to taste with salt and more parmesan.
Put the polenta mixture into moulds about ¾ inch/2 centemetres thick and leave for at least an hour.
Remove the polenta from the moulds and put on very lightly oiled foil on a grill pan. Sprinkle with a little parmesan and grill under a hot grill for about five to seven minutes. Turn, sprinkle with more parmesan and grill for a further five to seven minutes. Note: if you don't have moulds, use an oblong dish and cut into strips after an hour or so.