Preheat oven to 325°F (163°C). Prepare a 9-inch springform pan with parchment paper and grease the sides.
In a stand mixer, beat 16oz cream cheese and 0.66 cup sugar until smooth. Add 2 eggs, sour cream, and 1 tsp vanilla. Pour into the springform pan and bake for 50 minutes. Cool completely, then freeze for at least 3 hours to allow for easy assembly.
Preheat oven to 350°F (175°C). Grease and flour two 9-inch round cake pans.
Sift flour, 1.5 cups sugar, baking soda, cocoa powder, and salt into a large bowl.
In a separate bowl, whisk buttermilk, 2 eggs, vegetable oil, vinegar, 1 tsp vanilla, and green food coloring until well combined.
Gradually add the wet ingredients to the dry ingredients, mixing until just combined. Divide batter equally between the two prepared cake pans.
Bake cake layers for 25-30 minutes or until a toothpick comes out clean. Cool in pans for 10 minutes, then transfer to wire racks to cool completely.
Prepare frosting by beating 16oz cream cheese and butter until light and fluffy. Gradually add powdered sugar and 1 tsp vanilla; beat until smooth.
To assemble, place one green velvet cake layer on a serving plate. Place the frozen cheesecake layer on top. Top with the second green velvet cake layer.
Frost the top and sides of the cake with the cream cheese frosting. Chill for at least 1 hour before slicing.