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Preheat the oven to 350F. Line two baking sheets with parchment paper.
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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 ¾ teaspoon salt. Using a rubber spatula, fold in the flour.
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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.
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Meanwhile, using an electric mixer, cream the softened butter with the cream cheese. Add the powdered sugar, ½ teaspoon vanilla and the pinch of salt; mix on low speed until blended, then beat on medium-high speed until fluffy, about 2 minutes.
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Spread the flat side of 12 cakes with the cream cheese frosting. Top each with another cake.