3/4 cup (1 1/2 sticks) unsalted butter
1 2/3 cups all-purpose flour
2 teaspoon baking powder
1 teaspoon salt
1/2 teaspoon ground cinnamon
1/4 teaspoon freshly grated nutmeg
1/8 teaspoon ground cloves
1 cup pumpkin puree
1 cup packed light brown sugar
1/2 cup granulated sugar
2 large eggs, at room temperature
1 lb confectioners’ sugar, sifted divided
1/2 cup plus 1 tablespoon heavy cream
1 teaspoon vanilla extract
1/4 teaspoon salt
1 (8-oz) package cream cheese, at room temperature
1/4 cup (1/2 stick) unsalted butter, at room temperature
Preheat oven to 325 F. Line cupcake pans with paper liners.
Add the butter to a medium saucepan and set over medium-low heat. The butter will melt then begin to bubble and foam. Eventually it will start to turn brown and smell nutty – be patient and watch carefully, it can go from brown to burned quickly. Remove the pan from the heat and pour the butter into a small heatproof bowl to stop the cooking. Set aside to cool.
In a medium bowl, whisk together the flour, baking powder, salt, cinnamon, nutmeg and cloves. Grab a second medium bowl and add the pumpkin puree, brown sugar, granulated sugar, eggs and the cooled brown butter. Whisk until thoroughly combined. Add the dry ingredients to the bowl and whisk just until combined.
Divide the batter among the liners, filling each about 2/3 to 3/4 full. Bake for 20-25 minutes (rotating the pans halfway through), or until a toothpick inserted in the center comes out clean. Transfer the pans to wire racks and let the cupcakes cool for just a few minutes before removing them to the racks to cool completely.
To make the frosting: Add 1/2 cup of the confectioners’ sugar to a small nonstick skillet. Try to sprinkle in an even layer. Set the pan over medium heat and let the sugar sit untouched until it melts – it’ll seem like it takes forever to start melting, but once it gets going, it goes fast. Continue cooking until the sugar turns an amber color, stirring occasionally – keep an eye on it, it can burn quickly. Add 1/2 cup of the cream, the vanilla and salt (carefully, the mixture will bubble up!). Stir until any hardened bits of caramel melt. Add the remaining tablespoon of cream and stir to incorporate. Strain the caramel into a heatproof bowl and set aside to cool.
Combine the cream cheese and butter in the bowl of a stand mixer fitted with the paddle attachment. Beat on medium speed until light and fluffy. Gradually add the remaining confectioners’ sugar, stopping to scrape the sides of the bowl as necessary. Once all the sugar has been added, mix in the cooled caramel. Beat the frosting on medium speed until smooth and fluffy. Cover the chill until the frosting is firm enough to pipe (I think it was about an hour for me).
To assemble the cupcakes: Transfer the frosting to a pastry bag fitted with a tip. Pipe frosting into a swirl on each cupcake. Garnish with more caramel sauce or a caramel square, if desired.