Put the egg whites in a mixing bowl and beat slowly at first. As the egg whites thicken, add 1/4 cup of sugar and increase the beating speed until the whites hold very stiff peaks.

Scald the milk and add 1/4 cup of sugar and vanilla. Stir the mixture until the sugar has dissolved.

Poach the egg whites in milk for 4 to 5 minutes, turning once. The idea here is to drop large dollops of the beaten egg white/sugar mixture onto the surface of the milk until they are cooked through. These will be the "islands" for this exotic dessert. Remove to serving platter.

Beat the egg yolks with the remaining 1/2 cup of sugar in a bowl and add the hot milk, stirring vigorously. Cool and strain.

Make a caramel by boiling 1/2 cup of sugar and 1/2 cup of water to a syrup.

Serve the cooled milk-and-egg mixture with the islands and drizzle caramel on top.