Sorbet: Place a bowl or 2 sheet pans in the freezer to chill. Combine the water and sugar in a saucepan and bring to a boil. Whisk the juices together in another bowl. Let cool slightly, then whisk half the syrup into the juices and taste. Slowly add more syrup, tasting frequently. The mixture should taste definitely tart and sweet; you might not use all the syrup. Freeze in an ice cream machine, then transfer to the frozen bowl and keep frozen.

Ice Cream: Combine the milk with 1/3 cup of the sugar in a saucepan and heat just to a boil. Immediately remove from the heat. Whisk the egg yolks with the remaining 1/3 cup sugar until well combined. Whisk a few tablespoons of the hot milk mixture into the egg mixture, then pour back into the saucepan with the remaining milk mixture.

Cook over medium heat, stirring constantly with a wooden spoon. At 160 degrees F, the mixture will give off a puff of steam. When the mixture reaches 180 degrees F it will be thickened and creamy, like eggnog. Test it by dipping a wooden spoon into the mixture. Run your finger down the back of the spoon. If the stripe remains clear, the mixture is ready; if the edges blur, the mixture is not quite thick enough yet. When it is ready, quickly remove it from the heat. Strain the mixture into a bowl and place it in the ice bath to cool. Let cool, stirring often. When cold, whisk in the sour cream and freeze in an ice cream machine. When frozen, use a small ice cream scoop to make walnut-sized balls and freeze solid again.

To assemble, let the sorbet soften slightly. With a larger ice cream scoop, dig out flat globs of sorbet and pack it around the ice cream balls, covering completely. Freeze for 30 minutes.