Add the softened cream cheese to stand mixer. Using paddle attachment, beat on medium until smooth, about 4 minutes.
Add the sugar and beat on medium for 3 minutes.
Add the crème fraiche and heavy cream, Beat on low for 1 minute. Scrape down bowl, if necessary.
Add eggs one at a time and beat on low for 1 minute after each addition.
Add the vanilla bean paste and beat on low just until incorporated.
Pour the cheesecake batter over cooled chocolate chip cookie crust.
Place the springform pan into roasting pan. Place roasting pan on middle rack of preheated oven. Add enough water to the roasting pan to go about 1-inch up the side of the foil wrapped springform pan.
Bake the cheesecake for 45 to 50 minutes. Turn off the oven, do not open the door and let the cheesecake continue to bake while the oven cools, about 45 minutes. Remove the springform pan from the roaster and place on wire rack. Remove foil and cool cheesecake to room temperature.
Leave the cheesecake in the springform pan, cover with foil and refrigerate several hours, preferably overnight.
Unhinge springform pan and lift away. Remove cheesecake from bottom of springform pan.