In a small bowl, combine crushed ginger snaps, sugar, and 1/3 cup melted butter. Blend well. Press the crust with a spoon into a 10-inch springform pan. Make sure to cover the bottom and the sides evenly. Bake the crust at 350°F for 8-10 minutes, and then let it cool.
In a large bowl, mix cream cheese, cornstarch, and sugar until smooth. Add sour cream to the mixture. Beat in the eggs. Add apple butter and 3/4 cup butter, and beat until smooth. Pour the mixture into the prepared ginger snap crust. Bake at 350°F in a water bath for about 2 hours.