Begin by gathering all the necessary ingredients. Preheat the oven to 375°F (190°C). Prepare 24 muffin cups by greasing them or lining them with paper liners.

For the pumpkin cupcakes, sift together the all-purpose flour, baking powder, ground cinnamon, nutmeg, ginger, cloves, allspice, baking soda, and salt in a large mixing bowl. Set this mixture aside.

In another large bowl, use an electric mixer to cream together the white sugar, softened butter, and brown sugar until the mixture becomes light and fluffy. Incorporate the eggs one at a time, ensuring each is well blended before adding the next. Follow this by mixing in the pumpkin puree and milk. Gradually add the flour mixture, stirring until just combined. Divide the batter evenly among the prepared muffin cups, filling each about three-quarters full.

Bake in the preheated oven for approximately 25 minutes, or until the tops spring back when lightly pressed. Allow the cupcakes to cool in the pans for 5 minutes, then transfer them to a wire rack to cool completely, which should take around 20 minutes.

To prepare the frosting, beat the softened cream cheese and butter in a large bowl with an electric mixer until smooth. Gradually add the confectioners' sugar, mixing until fully incorporated. Add the vanilla extract and ground cinnamon, and continue to beat until the frosting is fluffy.

Once the cupcakes have cooled, frost them generously with the cinnamon cream cheese frosting.