Preheat oven to 350 degrees. Line a standard size muffin/cupcake tin with paper liners, set aside.
In a small mixing bowl, whisk together the flour, baking soda, baking powder, salt, cinnamon, and nutmeg.
In a medium mixing bowl, whisk together the oil, applesauce, sugars, egg, vanilla, and carrot. Mix in the dry ingredients just until combined, set aside.
In the bowl of a stand mixer (or a large mixing bowl with a hand mixer), beat the cream cheese for 1 minute or until smooth and creamy. Add the sour cream and mix to combine. Add the sugar, flour, egg and vanilla extract, mix just until combined.
Start by placing 1 tablespoon of cake batter into the bottoms of the liners, then add 1/2 tablespoon of cheesecake filling. Repeat the process one more time, ending with cheesecake on top. If you have leftover filling, divide it evenly between the liners.
Place in the oven and bake for 25-35 minutes or until the cheesecakes are set. Remove from the oven and allow to cool at room temperature for 30 minutes before transferring to a refrigerator to cool for 2 hours.
Before serving, top with homemade whipped cream, a dash of cinnamon and a sprinkle of toasted nuts. Keep refrigerated for up to 4 days.