Preheat the oven to 325°F (160°C). Line a 12-cup muffin tin with paper liners for easy removal.

In a mixing bowl, combine crushed graham crackers, melted butter, and 1 tablespoon of sugar. Mix until the graham cracker crumbs are evenly coated.

Press a tablespoon of the graham cracker mixture into the bottom of each muffin cup to form the crust. Use the back of a spoon to compact it.

In a separate bowl, beat the softened cream cheese with an electric mixer until smooth and creamy.

Gradually add ⅔ cup sugar, vanilla extract, and dried lavender. Mix until well combined.

Add the eggs one at a time, mixing well after each addition. Scrape down the sides of the bowl as needed.

In a food processor, pulse the blackberries until smooth. Strain through a fine mesh sieve to remove seeds, if desired.

Stir in the blackberry puree, lemon juice, and cornstarch into the cream cheese mixture until evenly combined.

Gently fold in the sour cream until fully blended into the batter.

Pour the cheesecake batter over the prepared crusts in the muffin tin, filling each cup to the top.

Bake in the preheated oven for 20 to 25 minutes, or until the centers are set but slightly jiggly.

Turn off the oven, crack the door open, and let the cheesecakes cool in the oven for an additional 15 minutes.

Remove from the oven, allow to cool at room temperature, then refrigerate for at least 2 hours before serving.