Preheat your oven to 325°F (160°C). Grease a 9-inch springform pan with cooking spray or butter.
In a medium bowl, combine the graham cracker crumbs, melted butter, and 1/4 cup sugar. Mix until well combined. Press the mixture firmly into the bottom of the prepared springform pan to form the crust.
In a large mixing bowl, beat the softened cream cheese with an electric mixer on medium speed until smooth and creamy, about 2-3 minutes.
Gradually add 1 cup of sugar and continue to beat until well combined.
Add the eggs one at a time, mixing well after each addition. Then mix in the vanilla extract.
In a small bowl, dissolve the instant coffee granules in the cooled brewed coffee. Add this mixture to the cream cheese batter and mix until fully incorporated.
Pour the cheesecake batter over the prepared crust in the springform pan.
Bake in the preheated oven for 50-60 minutes, or until the center is set but still slightly jiggly.
Remove the cheesecake from the oven and let it cool at room temperature for about 1 hour.
In a separate bowl, mix together the sour cream and heavy cream until smooth. Spread this mixture evenly over the cooled cheesecake.
Refrigerate the cheesecake for at least 4 hours, preferably overnight, to allow it to set completely.
Before serving, run a knife around the edge of the pan to loosen the cheesecake, then carefully remove the sides of the springform pan.