Preheat oven to 350°F (175°C). Line a 12-cup muffin pan with cupcake liners.
In a large bowl, cream butter, granulated sugar, and brown sugar until light and fluffy. Mix in eggs, vanilla, and pumpkin purée.
In another bowl, whisk together flour, cocoa powder, baking soda, baking powder, and salt.
Add dry ingredients to wet mixture alternately with buttermilk, mixing until just combined.
Divide batter evenly among liners. Bake for 18–20 minutes, or until a toothpick comes out clean. Cool completely.
For the frosting: Beat cream cheese and butter together until smooth. Add powdered sugar, pumpkin purée, pumpkin pie spice, and vanilla. Beat until fluffy.
Pipe or spread frosting onto cooled cupcakes. Serve immediately or refrigerate.
Notes
Store frosted cupcakes in the fridge for up to 4 days. Bring to room temperature before serving for best texture.