Preheat oven to 350°F (175°C) and line two 12-cup muffin tins with paper liners.
Whisk together flour, baking soda, baking powder, salt, cinnamon, ginger, cloves, and nutmeg in a medium bowl.
In a large bowl, whisk together eggs, granulated sugar, brown sugar, vegetable oil, and pumpkin puree until well combined.
Gradually stir the dry ingredients into the pumpkin mixture until just incorporated.
Divide the batter evenly into the prepared muffin cups, filling each approximately two-thirds full.
Bake for 20 to 22 minutes, or until a toothpick inserted into the center of a cupcake comes out clean.
Cool cupcakes in the tin for 5 minutes, then transfer to a wire rack to cool completely.
In a clean bowl, beat the softened cream cheese and butter until smooth and creamy.
Add powdered sugar and vanilla extract; beat on low speed until combined, then on high speed until light and fluffy.
Apply the frosting to the completely cooled cupcakes using a piping bag or spatula.