Position oven rack in center of oven. Preheat oven to 375 degrees F. Line 2 baking sheets with parchment paper and set aside.
Sift together flour, baking powder, soda, salt, cinnamon, ginger, allspice, and nutmeg onto a sheet of waxed paper.
Beat 7 tablespoons butter and brown sugar in a large mixing bowl at medium speed of an electric mixer until fluffy, scraping bowl as necessary. Add sweet potato, then eggs, beating until blended after each addition. Add half of flour mixture and half of buttermilk to creamed mixture; beat at medium speed just until blended. Add remaining half of flour and buttermilk and 1 teaspoon vanilla; beat until blended.
Using an ice cream scoop, drop batter into 18 mounds onto the prepared baking sheets, spacing them 2 inches apart. Or drop batter into 32 mounds by well-rounded tablespoons onto the prepared baking sheets. Bake, one baking sheet at a time, until cakes begin to crack and are firm to the touch, about 15 minutes. Remove from oven and slide the parchment paper, with the cakes, onto a wire rack to cool completely. Use a thin metal spatula to lift the cookies off the parchment paper.
Spread flat side of half of the cakes generously with Salted Peanut Cream Filling. Top with the remaining cakes, pressing down lightly to seal them together.
Salted Peanut Cream Filling
Beat cream cheese and 2 tablespoons butter in a large mixing bowl at medium-high speed of an electric mixer until fluffy, scraping sides of bowl as necessary. Beat in confectioners' and 1 teaspoon vanilla until smooth.
Pulse peanuts in a food processor until finely ground and they resemble dry breadcrumbs. Fold peanuts into cream mixture. Makes 1 1/2 cups