Decrease the temperature of the oven to 300 degrees Fahrenheit (148 degrees Celsius).
Combine cream cheese, sugar, and flour in a spacious bowl and mix on a low speed until fully blended and without lumps. It is important to use a low speed to avoid incorporating excess air into the mixture, as this could lead to cracks. Make sure to scrape the sides of the bowl to ensure everything is well mixed.
Gradually incorporate the sweetened condensed milk into the mixture and stir until thoroughly blended and silky. Occasionally scrape the sides of the bowl to ensure all ingredients are well mixed.
Combine the sour cream, coconut extract, and vanilla extract, and blend at a low speed until fully incorporated.
To create the mixture, add the eggs individually, taking your time to blend them in after adding each one. When necessary, use a spatula to scrape the sides of the bowl, ensuring that all ingredients are thoroughly combined.
Split the blend into two sizable bowls, ensuring equal distribution. Although my preference is to utilize a food scale for weighing the filling and achieving proportional division, you can also utilize measuring cups if a food scale is not available.
Combine the mango puree, mango flavor, and mango extract in one bowl and stir gently until fully mixed. In the other bowl, stir together the key lime juice until well combined.
To create an even layer, carefully pour the key lime filling onto the pre-baked crust and ensure it is spread evenly. Then, drizzle the mango filling on top of the key lime filling, making sure to distribute it evenly by pouring it around and over the key lime filling. Avoid pouring it all in one spot, as this will result in an uneven layer.
Put the springform pan into a larger pan. Pour warm water into the larger pan, making sure it reaches about halfway up the sides of the springform pan. Be careful not to let the water go above the top edge of the aluminum foil on the springform pan.
Place in the oven and bake for a total of 1 hour and 15 minutes. The middle part should be firm, yet slightly wobbly, while the outer edges should be more solid.
Switch off the oven and keep the door shut for half an hour. During this time, the cheesecake will carry on cooking but also start to cool gradually.
To prevent cracking, leave the oven door slightly open for 30 minutes after removing the cheesecake, allowing it to cool gradually.
Take out the cheesecake from the oven along with the water bath wrapping and let it cool down to approximately room temperature. Keep the cheesecake in the fridge until it becomes firm, which should take around 5 to 6 hours or you can leave it overnight. Take the cheesecake out from the springform pan and put it on a dish that will be used for serving. While you prepare the toppings, keep the cheesecake refrigerated.