Combine dry ingredients. In the bowl of a stand mixer, whisk together the bread flour, salt, and pumpkin pie spice until evenly combined.
Mix and knead. Add the pumpkin purée, active potato flake sourdough starter, 2 tablespoons melted butter (cooled slightly), warm water, and maple extract. Mix on low until combined, then increase to medium speed and knead until a smooth but very sticky dough forms. Scrape down the sides of the bowl as needed.
First fermentation. Transfer the dough to a large, lightly greased bowl. Cover with plastic wrap and allow to ferment at room temperature for 6–8 hours, or until doubled in size.
Prepare the pan. Melt 1 tablespoon of butter and brush over the bottom and sides of a 9x13-inch baking pan.
Transfer the dough. Place the fermented dough into the prepared pan. With lightly wet or buttered fingers, gently press the dough toward the edges of the pan. Do not dimple the dough yet.
Second rise. Cover with plastic wrap or a clean kitchen towel and allow to rise for 4–6 hours, or until doubled in size and the dough fills or nearly fills the pan.
Prepare topping. Near the end of the rise, preheat the oven to 450°F. Melt 5 tablespoons of butter in a small saucepan over low heat. Remove from heat and stir in the brown sugar, cinnamon, and pumpkin pie spice.
Top and dimple. Drizzle the cinnamon sugar mixture evenly over the risen dough. With wet or buttered fingers, press deep dimples across the entire surface. The dough may look messy after dimpling; this is normal.
Bake. Bake at 450°F for approximately 15 minutes, until golden and crusty. Check that the internal temperature of the bread reaches 190–200°F.
Cool. Allow the focaccia to cool in the pan for 10 minutes, then transfer to a wire cooling rack to cool completely.
Prepare frosting. In a small bowl, whisk together the powdered sugar, milk, vanilla extract, and salt until smooth. Add additional milk if a thinner consistency is desired.
Serve. Drizzle the vanilla frosting over the cooled focaccia. Slice and enjoy!