1 cup powdered sugar, sifted
1 cup (2 sticks) unsalted butter, room temperature
1 7-ounce jar marshmallow creme
2 teaspoons maple extract
3 cups all purpose flour
2 teaspoons ground cinnamon
1 1/2 teaspoons baking powder
1 1/2 teaspoons baking soda
3/4 teaspoon salt
3/4 teaspoon ground nutmeg
3/4 teaspoon ground cloves
6 tablespoons (3/4 stick) unsalted butter, room temperature
3/4 cup (packed) golden brown sugar
3/4 cup sugar
1/2 cup vegetable oil
3 large eggs
1 15-ounce can pure pumpkin
1/2 cup milk
Nonstick vegetable oil spray
Using electric mixer, beat sugar and butter in large bowl until fluffy, about 2 minutes. Add marshmallow creme and maple extract; beat until blended and smooth. DO AHEAD Can be made 2 hours ahead. Let stand at room temperature.Cake
Sift first 7 ingredients into large bowl. Using electric mixer, beat butter and both sugars in another large bowl until blended. Gradually beat in oil. Add eggs 1 at a time, beating to blend between additions. Beat in pumpkin. Add dry ingredients in 2 additions alternately with milk in 1 addition, beating to blend between additions and occasionally scraping down sides of bowl. Cover and chill batter 1 hour.
Arrange 1 rack in bottom third of oven and 1 rack in top third of oven; preheat to 350°F. Line 2 baking sheets with parchment; spray lightly with nonstick spray. Spoon batter onto baking sheet to form cakes (about 3 level tablespoons each; about 12 per baking sheet), spacing apart. Let stand 10 minutes.
Bake cakes until tester inserted into centers comes out clean, about 20 minutes, rotating sheets halfway through baking. Cool cakes completely on baking sheets on rack. Using metal spatula, remove cakes from parchment.
Line cooled baking sheets with clean parchment; spray with nonstick spray, and repeat baking with remaining batter.
Spoon about 2 tablespoons filling on flat side of 1 cake. Top with another cake, flat side down. Repeat with remaining cakes and filling. (If you wish to do the cookie part ahead of time, you may do so and store in single layer in an air tight container).