1. Preheat the oven to 325°F (165°C). Grease a 9-inch springform pan and line the bottom with parchment paper.

2. In a large bowl, beat the cream cheese with a hand mixer until smooth and creamy, about 2-3 minutes.

3. Gradually add in the 1 cup of sugar, beating well after each addition until the mixture is light and fluffy.

4. Add the eggs one at a time, beating well after each addition.

5. In a separate bowl, whip the heavy cream until stiff peaks form. Gently fold the whipped cream and vanilla extract into the cream cheese mixture.

6. Sprinkle the Earl Grey tea leaves over the batter and gently fold them in.

7. Pour the batter into the prepared springform pan and smooth the top.

8. Bake for 60-70 minutes, or until the center is still slightly jiggly. Turn off the oven and let the cheesecake remain in the oven for an additional 1 hour.

9. Remove the cheesecake from the oven and let it cool completely on a wire rack, then refrigerate for at least 4 hours or overnight.

10. For the blackberry sauce, combine the blackberries, 1/4 cup sugar, and lemon juice in a saucepan. Cook over medium heat, stirring occasionally, until the berries release their juices and the sauce thickens, about 10-15 minutes.

11. Serve the chilled London Fog Basque Cheesecake drizzled with the warm blackberry sauce.