Melt butter and pour over crumbs in a large mixing bowl. Mix ingredients together until crumbs are well saturated by butter. Press crumb mixture into pan and up sides of a 9-inch spring form pan. Bake in oven for 8-12 minutes until crust feels dry and firm.
Over a double boiler, melt chocolate. Once melted, mix heavy cream into the chocolate and set chocolate mixture aside to cool slightly.
In a kitchen mixer, beat the cream cheese to a smooth consistency. Mix in sugar and cornstarch. Beat in eggs and yolks a little at a time. Mix in the sour cream. Remove one cup of the batter into a separate bowl and set aside.
Add the chocolate mixture to the batter remaining in the mixer and mix to a smooth batter.
With the reserved batter in the separate bowl, add a few drops of peppermint extract and green food coloring and mix to incorporate.
Wrap the outside of the cooled spring form pan with cling wrap and then aluminum foil. This is to prevent water from seeping into the cake. Sit the spring form in a baking dish and pour the mint cheesecake batter into the spring form on top of the crust. Top with chocolate cheesecake batter and softly swirl into mint batter. Fill the baking dish with boiling water to come about half way up the spring form pan.
Bake in the water bath for approximately 35-45 minutes until the top of the cheesecake is firm but underneath is still slightly jiggly. Remove spring form from pan in oven and immediately remove foil and wrap. Allow the cheesecake to cool. Once cooled, cover top of spring form pan with plastic wrap and place in refrigerator overnight.