Preheat oven to 325°F (163°C) and line a 12-cup muffin tin with paper liners.

In a small bowl, combine graham cracker crumbs, melted butter, and 1 tablespoon sugar. Press 1 tablespoon of the mixture into the bottom of each liner.

In a small saucepan over medium heat, combine blackberries, 2 tablespoons sugar, and lemon juice. Simmer for 10 minutes until berries break down. Strain through a fine-mesh sieve to remove seeds and set the syrup aside to cool.

In a large bowl, beat the softened cream cheese and 1/2 cup sugar until smooth. Add eggs one at a time, followed by sour cream, ground lavender, and vanilla extract.

Divide the cheesecake batter evenly among the muffin liners.

Place 3 small dots of the blackberry syrup onto the top of each cheesecake and use a toothpick to swirl.

Bake for 18 to 22 minutes until the centers are slightly jiggly but the edges are set.

Remove from the oven and cool to room temperature, then refrigerate for at least 4 hours before serving.