Heat a large thick-bottomed saucepan over medium heat and whisk together milk, heavy cream, sugar, vanilla and instant espresso.

Continue whisking the milk until just before the milk begins to boil. You do not want the milk to boil, as it will curd and produce a lumpy egg nog. Remove the pot from heat.

In a bowl, whisk together all the egg yolks.

Slowly whisk 1 cup of the hot milk, a few tablespoons at a time, in to the egg mixture. This temper the eggs and keep the egg nog from getting lumpy.

Whisk in the tempered eggs with the remaining hot milk in the pot.
Heat the pot again over medium heat, whisking continuously until the cream mixture thickens, about 5-10 minutes. Remove the pot from heat.

Place chocolate chips in a microwave safe bowl.

Microwave the chocolate chips on high heat for 30 seconds. Stir the chocolate chips then heat again in the microwave high heat for 30 seconds.
Repeat until the chocolate has completely melted, about 2 minutes total.

Whisk in the melted chocolate into the hot milk mixture until thoroughly combined.

Return pot to medium heat to help combine the milk and the melted chocolate.

Remove the pot from heat and stir in brandy and whiskey.

Cool the egg nog to room temperature, transfer to a large pitcher, cover with plastic wrap and refrigerate until chilled, about 2 hours, or until ready to serve.