Pumpkin Cupcakes: Preheat the oven to 350°F and line a cupcake pan with 12 cupcake liners. In a stand mixer or large bowl with a handheld mixer, mix together the brown sugar, oil, eggs, and vanilla extract, until smooth and just combined.
In a separate medium-size bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, cloves, ginger, and nutmeg. Add the dry ingredients to the wet ingredients and mix until smooth. Add the pumpkin purée and mix until just combined. Fill each cupcake liner ¾ full.
Bake the cupcakes for 18-20 minutes or until a toothpick inserted in the middle comes out clean. Remove the cupcakes from the oven and leave in pan for 5 minutes to cool. Transfer the cupcakes to a wire rack to cool completely before frosting.
Cream Cheese Frosting: In a stand mixer or a medium-size bowl with a handheld mixer, combine softened cream cheese and softened butter; mix until smooth. Using a rubber spatula, scrape the sides of the bowl.
Add 2 cups powdered sugar and vanilla extract; mix until combined. Add the remaining 2 cups powdered sugar and mix until smooth. Scrape the sides and bottom of the bowl; mix to combine.
Assemble Cupcakes: Using the piping tip of your choice and a piping bag, fill the piping bag with the frosting. Frost each pumpkin cupcake with the cream cheese frosting. Refrigerate until ready to serve for up to 4 days.