Egg toppers, also known as egg scissors, are the perfect tool to create the eggshell cups used as serving vessels for our white-chocolate ice cream.
Using an egg topper, cut off wider end of each egg, or place each egg on its side on a kitchen towel, and use a serrated knife to saw halfway through wider end; remove egg yolk and white, then saw through remaining shells. Discard the eggshell tops; reserve whites and yolks of 2 eggs for the ice cream. Pour the remainder of the eggs in a container for another use, such as omelets or frittatas.
Place a large pot of water on the stove to boil. Rinse the insides of the eggshells under hot running water. Loosen the inner membrane around the opening of the eggshell, and carefully pull to remove the membrane. Discard the membrane. Dip the eggshells in the boiling water for 1 minute. Remove with a slotted spoon. Break off any loose bits of eggshell from around the edge, and make sure the opening is large enough for a teaspoon to fit through. Drain eggshells upside down on a clean towel. When eggshells are completely dry, turn them right side up, place in miniature muffin tins, and freeze.
Prepare an ice bath in a large bowl, and set aside. In a small heavy-bottom saucepan, combine half-and-half, 1/3 cup sugar, and the salt. Bring mixture to a simmer over medium-low heat, stirring occasionally, until the sugar is dissolved. Remove pan from heat, and add white chocolate. Stir until chocolate is melted.
In the bowl of an electric mixer fitted with the whisk attachment, beat the reserved 2 eggs with remaining 1/3 cup sugar on medium-high speed until a pale yellow color, about 4 minutes.
Reduce mixer speed to low. Gradually pour white-chocolate mixture into egg mixture, and continue to mix until just combined. Add heavy cream. Return mixture to saucepan. Continue cooking over medium heat, stirring constantly with a wooden spoon, until mixture has thickened slightly and clings to the back of spoon enough that a path remains in custard when you run your finger down the spoon, about 6 minutes. Remove pan from heat, and strain custard through fine-mesh sieve into medium bowl.
Place the bowl of custard into the prepared ice bath; stir occasionally until cool, about 10 minutes. (At this point, the custard can be covered and stored in the refrigerator up to 3 days before freezing.) Place the custard in an ice cream maker, and freeze, according to manufacturer's directions.
Transfer the ice cream to a pastry bag with no tip. Remove eggshells from freezer. Working quickly, pipe ice cream into shells; return shells to freezer.
Just before serving, place muffin tin of ice-cream-filled eggs in refrigerator for about 10 minutes, depending on firmness. This step tempers the ice cream to a softened stage and helps avoid breakage of the eggshell while eating. Place each egg into a nest, and serve immediately.