For the frosting, beat the butter and cream cheese in a large bowl with an electric mixer on medium-low speed until blended, 1 to 2 minutes. Add the confectioners’ sugar and beat until blended, 1 to 2 minutes. Scrape down the inside of the bowl; then add the pumpkin, pumpkin-pie spice, and vanilla extract and beat until blended, 2 minutes more. Spoon the frosting into a pastry bag or zip-top bag, seal the bag, and refrigerate the frosting until it is cold, at least 3 hours or up to 2 days. Makes about 3½ cups.
For the cupcakes, heat the oven to 350°F. Line a 12-cup muffin pan with cupcake papers.
In a large bowl, beat the butter and sugar with an electric mixer on medium speed until sandy in texture, 2 to 3 minutes. Add the eggs, one at a time, beating well after each addition. Beat in the pumpkin puree and vanilla extract.
In a medium bowl, whisk together the flour, cocoa powder, pumpkin-pie spice, baking powder, baking soda, and salt. Add the dry ingredients to the egg mixture alternately with the buttermilk and oil in three additions, beating on low speed after each addition.
Fill the muffin cups with batter and bake until a toothpick inserted in the center of one cupcake comes out clean, 20 to 25 minutes. Cool the cupcakes in the pan on a rack for 10 minutes. Remove them from the pan to cool completely on the rack.
Attach a tip to the pastry bag or snip off a corner from the zip-top bag, and squeeze the frosting onto the cupcakes.
Tip: For a brighter-orange color in the frosting, add nine drops of yellow food coloring and three drops of red along with the pumpkin.