Preheat the oven to 350 degrees.

In a medium bowl, combine the crust ingredients and mix together with your hands until just combined. Transfer the mixture to a 9-inch springform pan. Pat the crust down firmly in the bottom and up the sides approximately 2 inches. Bake in the oven for 10 to 12 minutes. Remove from oven to cool.

In the bowl of a stand mixer fitted with the paddle attachment, beat together the cream cheese and goat cheese until the mixture is light and fluffy. Add sour cream and beat until just combined. Add the 1 3/4 cups sugar and vanilla and beat again until combined. Add each egg in, one at a time, beating until well-combined after each addition. Pour the filling into the crust and bake for 1 hour, or until the center jiggles just slightly. Remove from oven and cool in the pan on a wire rack.

In a small saucepan, combine the blackberries, 1/2 cup sugar, and water. Bring to a boil over medium high heat and cook for approximately 5 minutes, stirring occasionally. Remove from heat and cool about 5 minutes. Pour the blackberry mixture on top of the cheesecake and set in the refrigerator to cool for at least 6 hours, ideally overnight.