Peel and coarsely chop the ginger. Wash 1 lime hot, dab dry and finely grate the peel. Heat 300 ml water, sugar, ginger and lime peel and simmer. Let it cool down. Halve 4 limes and squeeze them carefully.
Put the halves in the egg cardboard and freeze. Pour syrup through a sieve. Mix with the lime juice.
Place in a bowl and allow to freeze for about 1 hour, then stir well. Beat egg whites until stiff, fold in. Freeze for about 4 hours. Stir again and again until you have a portionable sorbet.
Use an ice cream scoop to make scoops. Freeze them for about 1 more hour. Just before serving, place the scoops on the frozen lime halves and serve immediately.