Peel the onions, leaving the root ends intact. Place in a pan of water, bring to the boil and simmer gently for 20 minutes. Remove and cool. Cut off and discard the top quarter of each onion, and scoop out a third of the inside. Combine the breadcrumbs, cheese, basil and butter in a bowl and season. Spoon into the onions and roast in a lightly greased baking dish for 50 minutes, or until the onions are soft.