Mix graham cracker crumbs, granulated sugar, and melted butter together until the mixture has a wet sand texture. Press this mixture firmly into the bottom of a greased springform pan to form an even crust. Set aside.

Steep the two Earl Grey tea bags in 1/4 cup of hot water for 10 minutes. Remove the bags and allow the tea to cool completely before using.

Beat the softened cream cheese and granulated sugar together until the mixture is very smooth. Add vanilla extract, cooled Earl Grey tea, and sour cream, mixing well after each addition. Finally, beat in the eggs one at a time just until blended to avoid overmixing.

Pour the prepared cheesecake filling over the graham cracker crust in the springform pan. Bake in a preheated oven at 325°F for 60 minutes, or until the edges are set and the center is slightly jiggly when gently shaken.

Remove the cheesecake from the oven and let it cool at room temperature for 1 hour. Afterward, transfer it to the refrigerator and chill for at least 4 hours or preferably overnight to set fully.

In a saucepan, combine mulberries, water, sugar, and lemon juice. Simmer over medium heat for 12 minutes until the mixture thickens to a jam-like consistency. Let cool.

Spoon the cooled mulberry sauce evenly over the chilled cheesecake. Slice into servings and enjoy this flavorful dessert.