Preheat oven to 350° F and line a muffin tin with cupcake liners. Set aside.
In a small bowl combine the flour, baking powder, baking soda, salt, cinnamon, allspice, ginger, and nutmeg. Whisk to combine.
In a large bowl with a hand mixer combine the sugar, eggs, pumpkin puree, extra virgin olive oil, and pure vanilla extract. Beat with the hand mixer until the mixture is thick and fully combined.
Fold in the dry ingredients, stir until just combined.
Portion out the batter equally into the 12 cupcake liners. This will fill the cupcake liners about ¾ full.
Bake for 23-25 minutes. Check that the cupcakes are fully cooked by using a cake tester or toothpick. If the toothpick comes out clean the cupcakes are ready.
Carefully remove the cupcakes from the muffin pan and transfer to a wire cooling rack. Let the cupcakes fully cool before icing them.
Cream Cheese Buttercream
In the bowl of a stand mixer fitted with the paddle attachment, add the softened butter and cream cheese. Beat on high for 2 minutes.
Scrape down the sides of the bowl.
1 cup at a time add the confectioners sugar. Beat on high for 2 minutes between each addition, and scrape down the sides of the bowl in between additions.
When all of the sugar is added, scrape down the sides of the bowl and add the pure vanilla extract and the heavy cream. Beat on medium-high for 1 minute.
Fit a piping bag with desired piping tip (I used a 1M piping tip in the above photos) and fill with the cream cheese buttercream.
Pipe buttercream onto cupcakes and top with a sprinkle of turbinado sugar (optional).Pipe buttercream onto cupcakes and top with a sprinkle of turbinado sugar (optional).
Transfer cupcakes to the refrigerator for a minimum of 30 minutes to let the icing set.
Notes
Cupcakes will keep at room temperature for 2-3 days or in the refrigerator in an airtight container for 3-4 days.