Preheat your oven to 325°F.

In a mixing bowl, combine the crushed graham crackers, melted butter, and sugar. Stir until well mixed, then press this mixture into the base of a 9-inch springform pan to create a solid crust.

Bake the crust for 10 minutes, then set aside to cool.

In another bowl, whip the softened cream cheese with the sugar until creamy. Incorporate the vanilla essence and mix thoroughly.

Add the eggs one at a time, blending on low speed just until combined to avoid overmixing.

Gently fold in the yogurt, fresh blueberries, and blueberry preserves. If desired, sprinkle in the activated charcoal and mix until the color is uniform.

Pour the cheesecake mixture over the cooled crust in the springform pan.

Bake for 50-60 minutes, or until the center is set but still has a slight jiggle.

Once done, turn off the oven and leave the door ajar, allowing the cheesecake to cool inside for an hour.

After cooling, let the cheesecake reach room temperature. Chill in the refrigerator for a minimum of 4 hours, or ideally overnight, before serving.