Preheat the oven to 350°. Line two baking sheets with parchment paper.
In a large bowl, whisk together the melted butter and brown sugar until smooth. Whisk in the eggs, pumpkin puree, pumpkin pie spice, 1 teaspoon vanilla, the baking powder, the baking soda and 3/4 teaspoon salt. Using a rubber spatula, fold in the flour.
Using an ice cream scoop or tablespoon, drop 12 generous mounds of batter, spaced evenly, onto each baking sheet. Bake until springy to the touch, about 10 minutes. Transfer to a rack to cool completely.
Meanwhile, using an electric mixer, cream the softened butter with the cream cheese. Add the confectioners' sugar and the remaining 2 pinches salt and 1/2 teaspoon vanilla; mix on low speed until blended, then beat on medium-high speed until fluffy, about 2 minutes.
Spread the flat side of 12 cakes with the cream cheese frosting. Top each with another cake.