Preheat your oven to 350°F. Lightly grease mini muffin tins.

In a large bowl, beat the softened butter, brown sugar, and granulated sugar together until creamy and smooth.

Add the pumpkin puree, egg, and vanilla extract, then beat until the mixture is light and fluffy.

In a separate bowl, whisk together the flour, cinnamon, baking powder, baking soda, salt, and nutmeg. Gradually add the dry ingredients to the wet mixture, stirring just until combined.

Fill each mini muffin cup about 3/4 full with the batter.

Bake for 17 to 20 minutes, until the cupcakes are set and a toothpick inserted in the center comes out clean.

Let the cupcakes cool in the tins for 5 minutes, then transfer them to a wire rack to cool completely.

In a large bowl, using an electric mixer on low speed, beat the softened butter, cream cheese, and vanilla extract until smooth and fully blended, about 1 minute.

Add the sifted powdered sugar, mixing until smooth, about 1 minute. Then add the cinnamon and ginger, and beat on medium speed for 1 to 2 minutes to lighten the frosting.