Preheat oven for 350 degrees F
In a food processor, pulse the graham crackers to crumbs. (Of course, you could also put graham crackers in a ziploc back and pound with a rolling pin.) Pour melted butter into graham cracker crumbs and combine together until crumbs are able to be pressed together and stick to one another.
Press graham cracker mixture into a silicone brownie bite pan, lined cupcake tin, or non-stick sprayed cupcake pan. You only need a thin layer in each bite, so the amount will vary depending on the size of bite you are making. My brownie bite pan required about a teaspoon and a half of crumbs for each bite. Set pan aside.
In a small saucepan, combine berries, water, and sugar, and simmer on medium-high heat. Stir occasionally, and cook for about 5-7 minutes or until mixture thickens. You'll want to keep an eye on it, as it may thicken sooner than this. Once it's a jelly-like consistency, remove from heat and set aside.
For the cheesecake mixture, combine cream cheese, Greek yogurt, and sugar in a medium sized bowl and mix until completely combined. Add vanilla. Add eggs, one at a time, mixing completely between each one.
Once mixed, drop about a Tablespoon (if using brownie bite size, like I did) on top of graham cracker crusts. When finished, add about a 1/2 a teaspoon of blackberry mixture into the cheesecake and swirl with a toothpick.
Bake at 350 for about 15-18 minutes, or until cheesecake is mostly solid. Let cool completely before removing from pan. Once mostly cool, you can place in the refrigerator overnight to finish setting.