Preheat oven to 350 degrees. Grease and flour two 8-inch round cake pans.
In the bowl of a stand mixer fitted with a paddle attachment, cream together the butter and sugar until fluffy. Beat in the eggs one at a time, being sure to scrape down the edges after adding each egg. Beat in the vanilla.
In another bowl, combine flour, espresso powder, cinnamon, ginger, baking soda, baking powder and salt. Slowly beat the dry ingredients into the wet ingredients. Once mixed, turn the mixer off and gently fold in the pumpkin puree.
Scoop batter equally into the cake pans and level with a knife. Bake in preheated oven for 30 - 35 minutes or until a toothpick inserted in the center comes out clean. Remove from oven and allow to cool for several minutes. Gently remove the cake from the pans and place on a cooling rack to cool completely, about an hour.
To make frosting cream together butter and 3 cups of powdered sugar. Add in cocoa powder, vanilla and coffee. Continue beating until a stiff spreadable mixture forms. If frosting is too thin, add the remaining powdered sugar.
Once cake has cooled, place one layer on a serving plater and spread 1/3 of the frosting on top. Place the second layer on top and frost whole cake with remaining frosting. Slice and serve.
If you store it in the refrigerator, allow to set at room temperature for at least an hour before serving.