Make the Cupcakes: Preheat oven to 350 degrees F. Line a 12-cup muffin pan with paper liners; set aside.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, nutmeg and cloves; set aside.
In a large bowl, whisk together the pumpkin, both sugars and the vegetable oil until completely combined, making sure to break up any chunks of brown sugar so no lumps remain. Whisk in the eggs, one at a time. Add the flour mixture in two additions, folding with a rubber spatula until no flour pockets remain.
Divide the batter between the baking cups, filling each about two-thirds full. Bake until a skewer inserted into the center comes out clean, 18 to 22 minutes. Allow to cool in the pan for 5 to 10 minutes, then remove to a wire rack. Allow the cupcakes to cool completely before frosting.
Make the Frosting: Using an electric mixer, beat the butter, powdered sugar, vanilla, and salt on low speed until smooth, then mix for an additional 2 minutes, scraping down the bowl as needed. Increase the speed to medium-low and add the cream cheese one piece at a time and mix until smooth, then mix for an additional 2 minutes.
Using a decorating bag and tip (I used the Ateco #827 tip) or an offset spatula, frost the tops of the cupcakes. (If you like the frosting piled high as pictured, this is the perfect amount of frosting. If you prefer less, you can scale the frosting down.) The cupcakes can stay at room temperature for a few hours, but should be refrigerated for longer-term storage up to 4 days.
Notes
Dark Brown Sugar - Adds a molasses flavor, but can substitute light brown sugar.
Canned Pumpkin - You want to look specifically for pumpkin puree, NOT pumpkin pie filling.
Cream Cheese - Use full-fat cream cheese that comes in a block (not the spreadable kind) - this will ensure that your frosting is not thin or watery. See post for frosting flavor variations.
Piping Tips: This set of jumbo tips is perfect for big swirls on top of cupcakes.
Storing - The frosted cupcakes can be stored in an airtight container in the refrigerator for up to 4 days. Unfrosted cupcakes can be kept in an airtight container at room temperature for up to 3 days before frosting and serving.
Freezing Cupcakes - It is recommended to freeze the cupcakes without the frosting. Once completely cool, they can be placed an airtight container or freezer-safe ziploc bag and frozen for up to 3 months. Thaw in the refrigerator overnight.
Make-Ahead Frosting - The frosting can be made up to 5 days in advance and stored in an airtight container or sealed piping bags in the refrigerator. It will firm up in the fridge, so allow to come to room temperature before piping on cupcakes.
Freezing Frosting - The cream cheese frosting can be kept in an airtight container in the freezer for up to 3 months. Thaw in the refrigerator overnight and then beat with a rubber spatula to smooth out.
Doubling the Recipe: You can double this recipe without issue.
Mini Cupcakes: You can make mini cupcakes out of this recipe; start checking the cupcakes around the 10-minute mark.