In a glass measuring cup, mix the eggnog and heavy cream together and set aside.

In a medium saucepan, whisk together sugar, cornstarch, salt, and ground nutmeg until evenly combined.

Whisk in the egg yolks with the dry mixture until you achieve a smooth mixture with no lumps.

Slowly pour the eggnog and cream mixture into the egg yolk mixture while whisking constantly to blend thoroughly without curdling.

Place the saucepan on the stove over medium heat. Stir the mixture constantly with a whisk or spoon, cooking for 8-10 minutes until it thickens enough to coat the back of a spoon and begins to boil. Continue boiling for an additional 30 seconds to activate the cornstarch fully.

Remove the pan from heat. Stir in the rum extract and unsalted butter pieces until melted and the pudding is smooth and glossy.

Pour the pudding through a fine mesh sieve into a bowl to remove any lumps. Cover the pudding bowl tightly with plastic wrap, pressing the wrap directly onto the surface of the pudding to prevent a skin from forming. Refrigerate for at least 4 hours or, preferably, overnight to set completely.

In a small saucepan over medium heat, combine 0.33 cup water and 0.33 cup sugar. Stir constantly until the sugar dissolves, then stop stirring and let the syrup simmer briefly. Pour the syrup into a bowl to cool for 5-10 minutes.

Add 1 cup of fresh cranberries to the cooled syrup, stirring to coat. Refrigerate overnight, stirring occasionally.

The next day, line a baking sheet with a Silpat or wax paper and place a wire rack on top. Use a slotted spoon to lift the cranberries from the syrup and spread them evenly on the wire rack to dry for about 1 hour.

Pour 0.67 cup sugar into a shallow dish and add a third of the cranberries, rolling or shaking them to coat in sugar. Shake off excess sugar and place back on the wire rack to dry for another hour. Repeat the process with the remaining cranberries. Store sugared cranberries in an airtight container in the refrigerator for up to 1 week.

When ready to serve, spoon chilled eggnog pudding into bowls or glasses. Top with whipped cream, freshly grated nutmeg, and sugared cranberries as garnish.