Reduce the oven temperature to 325°F.
In the bowl of a stand mixer fitted with the paddle attachment, beat the cream cheese until smooth and creamy. Scrape down the sides and bottom of the bowl. Whisk together the sugar and flour. With the mixer running on medium-low slowly add the sugar mixture. Beat until the mixture is smooth, scraping down the sides and bottom of the bowl as needed.
With the speed set on medium add the eggs, one at a time, beating just until the yolk disappears before adding the next. Scrape down the sides and bottom of the bowl, beat again to blend. Be careful not to over beat.
Add the liqueurs, vanilla, sour cream and green food color if using. Beat on low until combined. Scrape down the sides and bottom of the bowl, and beat again for another 5 seconds or until well blended.
Pour the batter into the prepared pan. Fill the outer roasting pan with enough hot tap water to come halfway up the sides of the springform pan.
Bake at 325°F until the center jiggles slightly, the sides start to puff and the surface appears dry, about 100 to 110 minutes. Tent the cheesecake with foil if the top is getting too brown.
Turn off the oven and prop the oven door open slightly using a pot holder or wooden spoon. Allow the cheesecake to cool in the hot water bath for 1 hour. Transfer to a wire rack and remove the foil. Slide a small thin knife around the inside edge of the pan to loosen the sides of the cheesecake. Leave the cheesecake in the springform pan and cool to room temperature, about 2 to 3 hours.
Once cooled, cover the cheesecake with foil or plastic wrap and refrigerate overnight or up to 24 hours.