In the bowl of your stand mixer fitted with the paddle attachment, or using a hand mixer, beat the cream cheese, granulated sugar, and light brown sugar on medium speed for 2-3 minutes until the mixture is smooth.
Scrape down around the sides of the bowl and add in the room temperature sour cream, vanilla bean paste, lemon juice, all-purpose flour, cinnamon, and salt. Beat on low speed until everything is incorporated and smooth.
With the mixer on low speed, add in the room temperature eggs one at a time followed by the singular egg yolk. Beat on low after each egg is added just until the mixture is combined. You do not want to over-mix the filling.
Using a large spoon or spatula, stir the mixture gently to release any bubbles that may have developed. Pour the cheesecake batter into the springform pan with your baked crust and using an offset spatula or the back of a spoon, smooth the filling out evenly. Place the cheesecake on a rimmed baking sheet prior to placing it in the oven. This will help protect from any leaking that may occur during baking.
Prior to placing the cheesecake in the oven you need to prepare a water bath. Place a metal roasting pan on a rimmed baking sheet and fill the pan halfway with boiling water Place the baking sheet holding the filled roasting pan on the lowest shelf in the oven.
Place the baking sheet holding the cheesecake on the center rack of the oven and bake at 325˚F for 30 minutes.
After the cheesecake has baked for 30 minutes, reduce the oven temperature to 250˚F. Crack the oven door open a couple of inches and bake the cheesecake with the door open for 5 minutes. After 5 minutes, close the oven door and bake the cheesecake for an additional 35-50 minutes. If the cheesecake appears to be browning on top, feel free to cover it loosely with a foil tent halfway through baking. You will know the cheesecake is ready when the edges appear to be set, but the cheesecake still wobbles slightly in the center if the pan is shaken gently.
Turn the oven off and crack the oven door open 2-3 inches. Leave the cheesecake in the oven to cool for 35 minutes. After 35 minutes, remove the cheesecake and allow it to cool completely to room temperature for at least 2 hours. Keeping the cheesecake in the springform pan, place it in the refrigerator and allow it to chill for at least 8 hours, preferably overnight.