In a small saucepan, combine the blackberries and sugar. Over medium-high heat cook until they begin to release their juices.
Stir often and Cook until thickened. Thin but not watery- more jam like.
Remove from heat. Place in freezer to fully cool.
Preheat oven to 350 °F. Grease an 8x8 baking pan.
Mix crushed Graham crackers and butter together and then press firmly into bottom of the baking pan.
Bake for 15 minutes and then set aside to cool.
Decrease oven to 300 °F
In a large bowl mix softened cream cheese and yogurt together fully. I just use a large mixing spoon or fork.
Add the sugar and mix until fully combined.
Next add in one egg at a time, mixing fully between each.
Add lemon juice, zest and vanilla bean paste (extract).
Now to assemble: Mix 1/2 cup cheesecake filling into the blackberry reduction previously cooked and cooled.
Dump the remaining cheesecake filling onto Graham cracker crust and spread evenly.
Spoon the blackberry reduction on the top of the cheesecake. Use a knife or toothpick to swirl it gently into the cheesecake. DO NOT MIX. You just want a slight swirl throughout the top.
You can bake as is or add additional fresh blackberries sprinkled on the top.
Place in 300 °F oven for 45-55 minutes or until edges are slightly brown and middle is still slightly jiggly.
After cheesecake is done. Turn oven off and leave in oven for 1 hour with door open slightly.
Once cheesecake is cooled put in the fridge overnight before slicing and serving. Cheesecake always gets better the colder it gets!