1. Prepare the Crust:
   Preheat your oven to 350°F (175°C).
   Mix the graham cracker crumbs, sugar, and melted butter until well combined.
   Press the mixture into the bottom and up the sides of a 9-inch springform pan.
   Bake for 10 minutes, then allow the crust to cool completely.
2. Make the Blackberry Coulis:
   In a saucepan over medium heat, combine the blackberries, sugar, and lemon juice.
   Cook until the berries are soft and the sugar has dissolved, about 10 minutes.
   Press the mixture through a fine sieve to remove the seeds, collecting the coulis in a bowl.
   Reserve part of the coulis for the filling and part for layering.
3. Prepare the Cheesecake Filling:
   Beat the cream cheese and sugar together until smooth.
   Add the eggs, one at a time, beating just until blended after each addition.
   Mix in the blackberry puree and vanilla extract until the color is uniform and no streaks remain.
4. Assemble the Cheesecake:
   Pour a thin layer of blackberry coulis over the cooled crust.
   Let it set in the fridge for about 10-15 minutes.
   Carefully pour the cheesecake filling over the set coulis layer.
   Bake at 325°F (160°C) for about 50-60 minutes, or until the center is set but slightly wobbly.
   Let the cheesecake cool completely, then refrigerate for at least 4 hours, or overnight for best results.
5. Final Touches:
   Once chilled and set, spread a thin layer of blackberry coulis over the top of the cheesecake.
   Decorate the perimeter with fresh blackberries for an elegant finish.

Serving: Carefully remove the cheesecake from the springform pan before serving.
Slice with a hot knife (dipped in warm water and then dried) for clean cuts.
Serve and enjoy your stunning, no-artificial-colorant blackberry cheesecake!