Preheat your oven to 350°F (175°C) and prepare two 12-cup muffin tins by lining them with cupcake liners.

In a large mixing bowl, whisk together the all-purpose flour, baking powder, baking soda, salt, ground cinnamon, and nutmeg until evenly combined.

In another bowl, beat together the softened unsalted butter, granulated sugar, and brown sugar using an electric mixer on medium speed for 3-4 minutes.

Add the eggs one at a time to the butter-sugar mixture, mixing well after each addition, then incorporate the applesauce and vanilla extract.

Gradually add the dry ingredient mixture to the wet ingredients, mixing gently on low speed until just combined.

Spoon the cupcake batter into the prepared cupcake liners, filling each about two-thirds full.

Place the cupcake tins in the preheated oven and bake for 20 to 25 minutes.

Once baked, remove the tins from the oven and let them cool in the pan for about 5-10 minutes, then transfer to a wire rack to cool completely.

Prepare the cream cheese frosting by beating together cream cheese and butter until smooth, then gradually add powdered sugar.

Once the cupcakes are completely cool, generously frost each one with the cream cheese frosting.