In a medium saucepan, blanch lemons for 2 minutes to remove wax. Set aside.
To make the Crust: Preheat the oven to 350°F. Grease 2 7-ounce ramekins. In a blender, combine crackers, sugar, and zest from 1 blanched lemon. Blend in butter. Divide mixture between the prepared ramekins, pressing firmly. Bake until crust is lightly browned, 10 to 12 minutes.
To make the Cheesecake: Reduce the oven to 325°F. Make sure all cheesecake ingredients are at room temperature. Pat Mozzarella cheese dry. In a blender, combine Mozzarella cheese, cream cheese, cream, sugar, vanilla, zest of other blanched lemon, and ½ teaspoon juice from blanched lemons and blend (mixture will be crumbly). Add egg and egg yolk and blend just until smooth.
Add mixture to the ramekins. Arrange ramekins in a larger baking pan and add hot water to reach halfway up the sides of the ramekins. Loosely cover with foil and bake for 10 to15 minutes. To check for doneness, jiggle the pan slightly. Cheesecakes should jiggle but not lose their shape. If center holds, cheesecakes are done; if not, bake another 5 minutes or so. Remove the ramekins from the water bath and set aside to cool at room temperature for up to 4 hours. For best results, refrigerate overnight.
To make the Topping: In a blender, combine blackberries and ½ tablespoon juice from blanched lemons. Strain, then whisk in sugar.
To serve and garnish: Spoon topping on cheesecakes and garnish with cheese pearls and blackberries.
