Make the cupcakes. Position a rack in the middle of the oven. Preheat the oven to 325°F. Line 12 muffin tin cups with paper cupcake liners.
Sift the flour, baking powder, baking soda, salt, cinnamon, and ginger into a medium bowl and set aside. In a large bowl, using an electric mixer on low-medium speed, beat the melted butter, sugar, and pumpkin until smoothly blended. Mix in the eggs and crystallized ginger. On low speed, mix in the flour mixture until it is incorporated. The batter will be thick. Fill each paper liner with a generous ¼ cup of batter, to about ½ inch below the top of the liner. Bake just until the tops feel firm and a toothpick inserted in the center comes out clean, about 25 minutes. Cool the cupcakes for 10 minutes in the pan on a wire rack.
Carefully place the wire rack on top of the cupcakes in their pan. Protecting your hands with pot holders and holding the pan and rack together, invert them to release the cupcakes onto the wire rack. Turn the cupcakes top side up to cool completely.
Frost the cupcakes. Transfer ¼ cup of the frosting to a small bowl, and stir in enough cinnamon to make the frosting a light brown color and enough milk to make a thick but pourable frosting. Set aside to use for the spiderweb decoration. Use a small spatula to spread a scant 1/4 cup of the remaining frosting on top of each cupcake in a smooth even layer. Cleaning the spatula often against the side of the bowl will help you spread the frosting smoothly.
Spoon the reserved cinnamon frosting into a small self-sealing freezer bag. Press out the excess air and seal the bag. Cut a tiny hole in one corner of the bag, about 1/16 inch long. Hold the bag about ½ inch above a cupcake and slowly pipe 2 circles, one inside the other, on the frosting. Pipe a dot of the frosting in the center. Using a toothpick, and beginning at the center, draw the tip gently through the frosting toward the edge of the cupcake. Move the toothpick about ¾ inch away and, beginning at the edge of the cupcake, draw it toward the center. Continue pulling shallow lines, alternating the direction of the toothpick, around the top of the cupcake, to form a web pattern. Repeat with the remaining cupcakes.
The cupcakes can be loosely covered and stored at room temperature for up to 3 days.