Preheat the oven to 350 degrees F. Line 2 regular size cupcake pans with cupcake liners.

In a large bowl, whisk together the flour, pumpkin pie spice, baking powder, baking soda, cinnamon, ground cloves, and salt. Set the bowl aside. In a large bowl using an electric mixer on low speed, combine the sugar, oil, applesauce, vanilla extract, and pumpkin. Add the eggs 1 at a time. Mix on low until combined. Gradually add the flour mixture until just combined.

Fill the cupcake liners three-quarters full with batter and bake until the cupcakes spring back when touched with your finger, about 20 minutes. Let cool in the pans for a few minutes, and then remove to a wire rack to cool completely.

In a saucepan, heat 1/2 cup butter over medium-low heat until lightly browned, about 8 minutes. Cool. In a large bowl using an electric mixer on medium speed, beat the remaining 1/2 cup butter for 30 seconds. Add the cooled brown butter and beat until combined. Add the powdered sugar and vanilla. Beat in the buttermilk, 1 tablespoon at a time, until spreadable.