In a saucepan off the heat, combine cornstarch and sugar. Add egg and mix thoroughly. Stir in eggnog.
Bring to a boil over medium heat while stirring and scraping the bottom of the pan. Simmer for about 1 minute or until mixture thickens.
Remove from the heat. If necessary, pass through a sieve and pour into a bowl. Cover with plastic wrap directly on the surface of the cream. Let cool. Refrigerate while preparing crust.
In a food processor, combine flour, sugar and salt. Add butter and pulse until the mixture is the size of peas. Add milk and egg yolk and pulse until a ball begins to form. Form into a disk with your hands.
On a floured work surface, roll dough into a 40 x 15-cm (16 x 6-inch) rectangle. Line in a rectangular 35 x 10-cm (14 x 4-inch) pie plate. Place in the freezer for 15 minutes or refrigerate for 30 minutes.
With the rack in the middle position, preheat the oven to 200° C (400° F).
Pour eggnog mixture into cold crust. Place on a baking sheet and bake for about 20 minutes or until pastry cream is firm and crust is golden brown. Let cool on a wire rack. Refrigerate for about 3 hours.
In a saucepan, bring water and sugar to a boil. Add cranberries, remove from heat and let cool in the pan for about 20 minutes. Cook again over low heat for 5 minutes. Remove from the heat. Let cool and refrigerate until completely chilled, about 1 hour.
When ready to serve, pour cranberries and syrup over pie.
Candied cranberries can be prepared in advance and stored in an airtight container in the refrigerator for several days.