Preheat the oven to 350F/176C. Line a 12-cup muffin tin with cupcake cases, and set aside.
In a medium bowl, sift together the flour, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg. Set aside.
Using a hand or stand mixer, mix together the sugar and pumpkin puree until smooth. Alternating, beat in the dry ingredients, and milk on low speed, starting and ending with dry ingredients.
Divide batter between the cupcake cases, filling 3/4 full. Bake for 15 - 18 minutes, or until a toothpick inserted in the centre comes out clean. Let cool in the pan for about 5 minutes, or until cool enough to handle, then transfer to a wire rack to cool completely before filling and frosting.
For the Nutella Sauce
To make a hole in the cupcake, use a pairing knife to make a deep circular (1-inch in diameter) cut in the centre of the cupcake. Make sure you only cut about halfway through the cupcake. Using the tip of the knife, lift the cut piece of cake and remove it completely. Cut off the bottom half of the cut piece of cake, set it aside, or eat it. Set aside the top half of the cake piece, which will be used to cover the cupcake after filling them.
In a medium bowl, whisk together the Nutella and milk until completely smooth.
Using a small spoon or a piping bag, pour the Nutella sauce into each cupcake, filling almost to the top. Use the set-aside piece of cake to cover the tops of the cupcakes, where they have been filled.
For the Nutella Frosting
Using a hand or stand mixer, beat together the cream cheese and butter until smooth. Add the icing sugar, Nutella and vanilla, then mix until smooth and creamy. Transfer to a piping bag with a decorating dip and frost the cupcakes. Decorate with sprinkles if desired.