In a stand mixer fitted with the paddle attachment, cream together the cream cheese and sugar on medium low speed. Scrape the mixture off the sides of the bowl and make sure it is very smooth. Mix in the sour cream. Add the yolks one at a time, mixing well between each one. Add the mint extract and whiskey and mix until well combined.
Divide the cheesecake batter into two bowls and add the mint-cream mixture to one of the bowls.
Add about 1 cup of the white cheesecake batter to the prepared pan. Then add 1 cup of the mint batter in the center, do not spread it out too much.
Add about ¾ cup of the white batter, followed by ¾ cup of the mint batter.
Add about ½ cup of the white batter, followed by ½ cup of the mint batter.
Add about ¼ cup of the white batter, followed by ¼ cup of the mint batter.
Add about 2 tablespoons of the white batter, followed by 2 tablespoons of the mint batter.
Tightly wrap the spring form pan with foil and then bake the cheesecake in a hot water bath, tented with foil. Be sure the water you pour into the pan is nice and hot, so that it gets up to the oven temperature as soon as possible. This will help the cake to bake evenly. Bake for about 45 minutes, but check it after 30 minutes. It is done when the center is set and giggles like jell-o. Allow the cake to cool for 15 minutes, still sitting in the water bath.
Remove the pan from the water and foil.
Mix together the sour cream, sugar and vanilla. Spread the mixture over the top of the cheesecake and return to the oven for 10 minutes.
Before the cake cools, run a paring knife around the edge so that the cake can shrink away from the pan without cracking.