Preheat the oven to 350° F. Line a 12 cup muffin pan (or a 24 cup mini muffin pan) with baking cups.
PREPARE THE CUPCAKES:
In a large mixing bowl, whisk together the flour, baking powder, cinnamon, nutmeg, ginger and salt. Set aside.
In a separate bowl, stir the oil and sugar together. Whisk in the eggs, and stir in the vanilla extract.
Pour the wet ingredients over the dry ingredients and stir until just combined. Stir the pumpkin into the batter until it is thoroughly combined.
Spoon the batter into the lined muffin cups. Bake for 20 minutes, or until a knife inserted in the middle of a cupcake comes out clean. Less time will be needed if you are making mini-cupcakes. When cupcakes are removed from oven, let them sit for about 10 minutes, then remove them to cool completely on a wire rack.
PREPARE THE FROSTING:
In a medium bowl, use an electric mixer to mix the frosting ingredients until smooth. If you're going to pipe the frosting onto the cupcakes with a piping bag, you may wish to add a little more powdered sugar (1/4 cup at a time) until you have your desired thickness. Frost the cooled cupcakes.