Purée fresh blackberries in a blender until smooth, then strain through a fine mesh sieve to remove seeds. In a saucepan, combine strained blackberry purée with sugar and cornstarch. Cook for about 5 minutes, stirring until thickened and bubbling. Remove from heat and cool completely.

Combine graham cracker crumbs and sugar in a bowl, then stir in melted butter until incorporated. Line muffin tin with cupcake liners and press crumb mixture into bases. Preheat oven to 325°F (162°C) and bake crusts for 5 minutes or until golden. Allow to cool.

Beat cream cheese and sugar until smooth and creamy. Gradually mix in flour, sour cream, lavender extract, vanilla extract, and eggs, blending until silky. Optionally, add violet gel coloring.

Fill each crust with cheesecake batter evenly. Bake at 300°F (148°C) for 18-20 minutes until centers are slightly jiggly. Remove from oven.

Turn off oven and let cheesecakes cool inside for 10 minutes. Crack oven door and cool for another 15-20 minutes before transferring to room temperature and refrigerate for at least 2 hours to set.

Top cooled cheesecakes with blackberry topping. Whip heavy cream with powdered sugar until soft peaks form and pipe onto cheesecakes. Garnish with fresh blackberries.