Preheat oven to 350°. Line two baking sheets with parchment paper.

In the bowl of a standing mixer with whisk attachment, mix together butter and brown sugar until smooth. Add eggs, pumpkin purée, spices, vanilla, baking powder, baking soda, and salt. Using a spatula, fold in flour.

With an ice-cream scoop, drop 6 generous mounds of batter, spaced evenly, onto each of two baking sheets. Bake until springy to the touch, about 10 minutes. Transfer to a rack to cool completely
 

In the bowl of a standing mixer or with an electric beater, cream together cream cheese and butter. Add vanilla, maple syrup, powdered
sugar, and salt.

Mix on low speed until blended; then beat on medium-high speed until fluffy, about 2 minutes.

Spread the flat sides of 6 cakes with cream-cheese frosting. Top each with another cake.