Thoroughly grease a mini cheesecake pan. Place the graham crackers in the bowl of a food processor and pulse until finely ground. Add in the melted butter and pulse until moistened. Divide the mixture among the cavities of the cheesecake pan, about 1 heaping tablespoon in each. Firmly press into the bottom of each cavity (a shot glass or other small object makes easy work of this). Set aside.

In the bowl of an electric mixer, beat the cream cheese and sugar on medium-high speed until creamy and well combined. Add in the cream, lemon juice, and preserves and continue beating for 2 to 3 minutes, until well combined and thickened, with a texture similar to frosting. Divide the mixture among each cavity and cover with plastic wrap.

Chill until firm, at least 4 hours or overnight. The cheesecake can be stored in the fridge in an airtight container for up to 2 days.

Combine the berries, sugar, and lemon juice in the bowl of a blender or food processor and pulse until pureed. Top each cheesecake with a dollop of the sauce. Garnish with a more fresh blackberries. Serve.