Step 1: Prepare the Carrot Cake Base

1. Preheat your oven to 350°F (175°C). Line a mini muffin tin with paper liners or grease it well to prevent sticking.
2. In a medium bowl, whisk together flour, baking soda, baking powder, salt, cinnamon, and nutmeg. Set aside.
3. In a separate bowl, whisk together oil, applesauce, brown sugar, egg, and vanilla extract until smooth.
4. Gradually add the dry ingredients to the wet ingredients, stirring until just combined.
5. Fold in the grated carrots, making sure they are evenly distributed in the batter.

Step 2: Make the Cheesecake Layer

1. In a mixing bowl, beat the softened cream cheese until smooth and creamy.
2. Add the sugar, egg, and vanilla extract, and beat until well combined.

Step 3: Assemble the Cheesecake Bites

1. Fill each muffin cup about halfway with the carrot cake batter.
2. Spoon a small amount of cheesecake mixture on top of each, spreading it gently to cover the carrot cake layer.
3. If desired, sprinkle chopped walnuts or pecans on top for extra crunch.

Step 4: Bake the Cheesecake Bites

1. Bake for 20-25 minutes, or until the cheesecake layer is set and slightly golden.
2. Remove from the oven and let the bites cool in the pan for 10 minutes before transferring them to a wire rack to cool completely.

Step 5: Chill and Serve

1. Once cooled, refrigerate the bites for at least 2 hours to allow the cheesecake layer to firm up.
2. Dust with powdered sugar before serving for a beautiful finishing touch.