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For the cupcakes:
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1. Preheat the oven to 350 F and arrange the rack to the middle of the oven.
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2. Line 18 cups of two standard size muffin pans with paper liners or coat well with non-stick baking spray.
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3. In a large bowl (not the mixer bowl) sift together the flour, baking powder, cinnamon, cloves, allspice, nutmeg, baking soda and salt.
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4. Into the bowl of a stand mixer place the sugar and vegetable oil. Using the paddle attachment, beat on medium speed for about 1 minute until the sugar is fully incorporated into the sugar. Scrape down the sides of the bowl with a spatula.
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5. Add the eggs one at a time into the mixer bowl and beat well after each one is added.
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6. With the mixer on low, add the pumpkin and the vanilla pudding mix and beat until just combined.
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Scrape down the sides with a rubber spatula.
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7. With the mixer on low, add the dry ingredients slowly and beat for 1 minute until almost completely incorporated.
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8. Remove the bowl from the mixer and use a spatula to finish mixing the ingredients. Make sure to scrape down the edges again and to mix the ingredients at the bottom of the bowl.
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9. Fill the muffin cups to 3/4 full.
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10. Place muffin tins side by side in the oven and bake for 10 minutes.
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11. Very gently, turn the pans around and bake until a toothpick inserted in the center comes out clean, about another 10 minutes. Remove from oven.
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12. Allow cupcakes to cool in the pans on a wire rack for 5 minutes and then remove the cupcakes from the pans and cool completely before frosting.
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For the icing:
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1. If you haven't already, set out the cream cheese and unsalted butter to allow to come to room temperature.
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2. If you haven't already, sift the powdered sugar. Add the spices into the sugar and mix to combine.
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3. Place cream cheese and butter into the bowl of a stand mixer fitted with the paddle attachment and beat on medium until fully combined and smooth, about a minute.
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4. Reduce to low speed and very slowly add the sifted powdered sugar and beat for another 3 minutes until fully incorporated and smooth.
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5. Scrape down the sides of the bowl and make sure to incorporate the ingredients from the bottom of the bowl.
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6. At low speed, add the pumpkin and mix for one minute until smooth. If icing seems too loose, add more powdered sugar 1/4 cup at a time until you reach your desired consistency.
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7. Place in the refrigerator for 10 minutes and then use immediately.
