Reduce the oven temperature to 300°F (148°C).
In a large mixing bowl, combine the cream cheese, sugar, and flour. Using a low-speed setting on an electric mixer, blend until the mixture is smooth and free of lumps. Keeping the speed low minimizes air incorporation, preventing cracks in the cheesecake. Scrape down the bowl as needed to ensure even consistency.
Mix in the sour cream, cinnamon, and vanilla extract, stirring until fully integrated. Add the eggs one at a time, gently mixing after each addition. Scrape down the sides of the bowl as needed to achieve a silky, uniform batter. Set aside.
For the cinnamon filling, combine the brown sugar, cinnamon, and flour in a separate bowl. Pour in the melted butter and mix until the consistency resembles a thick, spreadable paste.
Sprinkle about a quarter of the cinnamon filling over the cooled crust. Drizzle a third of the cheesecake filling over the cinnamon layer, ensuring an even spread. Repeat this process twice more, alternating between cinnamon filling and cheesecake batter, creating distinct layers. Finish by sprinkling the remaining cinnamon mixture over the top.
Place the prepared springform pan inside a larger baking dish. Carefully pour warm water into the outer dish, ensuring the water reaches about halfway up the sides of the springform pan, but does not overflow onto the foil.
Bake for 1 hour and 20 minutes. The cheesecake should appear set but still slightly wobbly in the center.
Turn off the oven and leave the cheesecake inside with the door closed for 30 minutes. This allows the residual heat to continue cooking the cheesecake while gradually reducing the temperature. Afterward, crack the oven door open slightly and let the cheesecake cool inside for another 30 minutes. This slow cooling process helps prevent surface cracks.
Remove the cheesecake from the oven and carefully take it out of the water bath. Let it sit at room temperature until it cools completely, then transfer it to the refrigerator for at least 4-5 hours or overnight to firm up.