Process cookies in a food processor or place the cookies in a ziploc bag and smash with a rolling pin until they resemble fine crumbs. Mix in melted butter until the crumbs are moist. Tip the crust into a 16-cm diameter x 4.5-cm tall (6-inch x 2-inch) cake tin with a removable base (or a cake ring or a springform tin). Press the crumbs onto the bottom and sides of the cake tin - the sides will come up to 4-cm (1.5-inch) tall. Chill in the refrigerator while you make the Chocolate Ganache.
Make the Chocolate Ganache
Finely chop the dark chocolate. Place the chopped chocolate and instant coffee in a bowl. Place cream in a small pot and bring to a simmer. Pour the cream over the dark chocolate, cover with plastic wrap and set aside for 5 minutes. Whisk with a wire whisk until chocolate has completely melted and the mixture is smooth. Stir in the rum.
Alternatively, microwave chocolate, cream and instant coffee in 30-seconds intervals, stirring every interval, until chocolate has melted and mixture is smooth. Stir in rum.
Pour half of the Chocolate Ganache mixture into the Cheesecake Crust. Reserve the other half for the topping later on.
Freeze the Cheesecake Crust for 30 minutes.
Make and Bake the Cheesecake
Preheat oven to 175C / 350F. Whisk instant coffee, rum and vanilla in a small bowl until coffee has dissolved. Set aside.
Place the softened cream cheese and sugar in a mixing bowl. Beat on low speed with a handheld electric mixer (or you can mix manually with a wooden spoon) until the mixture is creamy - the sugar granules won't dissolve completely but it's okay. With the mixer on low, beat in the coffee-rum-vanilla mixture, egg and lastly flour, until everything is well-mixed together. Don't beat for too long as you don't want to incorporate too much air in the cheesecake batter.
Pour the cheesecake batter into the frozen Cheesecake Crust. Bake in the middle rack for 45 minutes to 1 hour, until the cheesecake jiggle slightly in the center.
Place the baked cheesecake on a wire rack and let cool for 30 minutes.
If the remaining chocolate ganache has hardened, heat it up gently over a double boiler or in a microwave until it's runny. Pour the ganache over the cheesecake and spread to cover the top completely.
Chill the cheesecake in the refrigerator for at least 4 hours until completely cold, preferably overnight.
Serve the Cheesecake
Run a thin spatula or thin knife around the cheesecake and remove the cheesecake from the cake tin. Dip a knife in hot water, wipe dry and slice the cheesecake for a clean cut.
Leftover cheesecake can be stored in an airtight container in the refrigerator for up to 5 days.