Peel the onions, but do not remove the roots, or the onions will fall apart while cooking.
Place in a single layer in a pan with a lid.
Add the butter, tomato purée and 300ml water
Bring to the boil and simmer very gently, with the lid on, for about half an hour.
Add the sugar, vinegar and seasoning.
Mix well and continue simmering, with the lid on, for a further half an hour until the onions are cooked through and very soft.
Now remove the lid and simmer faster, until the sauce is reduced down to a thick coating sauce.
Italians say to serve the onions at room temperature. I think that that would work better at the hot temperatures of Puglia, where this recipe comes from. Personally, I prefer them warm.It would work fabulously as part of a vegetarian trio, with, for instance, beans with sesame and hazelnuts, and garlic mushrooms.This would work well with any firm vegetable. So I would try carrots and swede, turnip and potatoes. You could add herbs too if you like. I think rosemary would be nice.