Preheat oven to 180 degrees C. Grease a baba tin with melted butter.
Beat butter, rind and sugar until light and fluffy. Beat in egg yolks, cheese and milk. Stir in sifted flour. Beat egg whites until stiff peaks form then fold into the cake in two batches. Spread into the tin then bake for about 1 hour. Let cake stand about 5 minutes before turning onto a wire rack.
Stir lime juice, water and sugar in a small saucepan over low heat until sugar dissolves; bring to a boil. Boil uncovered for 2 minutes or until syrup thickens slightly. Pour hot syrup over the cake.