Preheat oven to 350°F (175°C). Line two 8-inch square pans with parchment and lightly grease.
Whisk flour, baking powder, baking soda, cinnamon, pumpkin pie spice, and salt in a bowl.
Beat butter, granulated sugar, and brown sugar until creamy. Add eggs one at a time, then mix in pumpkin and vanilla.
Add the dry ingredients alternately with buttermilk, mixing just until combined. Divide the batter between the prepared pans.
Mix the melted butter, brown sugar, flour, cinnamon, pumpkin pie spice, and salt for the cinnamon swirl. Spoon over the batter and gently swirl with a knife.
Bake for 27–31 minutes, until a toothpick comes out with a few moist crumbs. Cool completely.
Beat cream cheese and butter until smooth. Add powdered sugar, vanilla, cream, and salt, then beat until creamy.
Place one cake layer on a serving plate. Spread the cream cheese filling evenly over the top, then add the second cake layer.
Whisk the powdered sugar, maple syrup, milk, vanilla, and cinnamon for the glaze. Drizzle over the top of the cake.
Chill for 30 minutes for cleaner slices, then cut into squares and serve.