Step 1Heat the oven to 325 degrees. Place a cake dish filled with water on the bottom rack.
Step 2Place the graham cracker crumbs in a medium bowl. Slowly pour the melted butter over the crumbs, stirring with a fork. Add 2 tablespoons whole black sesame seeds and mix.
Step 3Spread the mixture into a buttered 8-inch springform pan, patting it onto the bottom and about an inch up the sides of the pan, then pressing firmly with the bottom of a glass. Refrigerate while you prepare the filling.
Step 4In the bowl of an electric mixer, beat the softened cream cheese until smooth. Beat in three-fourths cup plus 2 tablespoons sugar. Add 2 cups sour cream and beat. Beat in the eggs one at a time. Try not to over-beat.
Step 5Divide the filling into two bowls. Combine the green tea powder and a little of the filling from one bowl and mix until smooth. Return the green tea mixture to one bowl of filling and mix to combine evenly.
Step 6To the other bowl of filling, add 2 teaspoons whole black sesame seeds and 2 teaspoons ground black sesame seeds and combine thoroughly.
Step 7Pour the green tea filling into the chilled crust. Carefully spoon the black sesame filling over the green tea layer. Smooth with an offset spatula.
Step 8Place the cheesecake on the center rack of the oven and bake for about 1 hour, 15 minutes. The edges should be set, but the center will be a little wobbly.
Step 9Turn the oven off and let the cake cool about 5 minutes with the oven door propped open with a wooden spoon.
Step 10Meanwhile, prepare the topping. Mix the remaining 1 cup sour cream with the remaining 2 teaspoons sugar and the vanilla.
Step 11Remove the cheesecake from the oven. Remove the pan of water and heat the oven back up to 425 degrees. Spread the sour cream mixture over the black sesame layer with an offset spatula. Bake for 8 minutes.
Step 12Allow the cheesecake to cool to room temperature, about 2 hours, on a rack before transferring it to the refrigerator. Refrigerate overnight to set. Before serving, sprinkle with the remaining whole black sesame seeds.