In the bowl of a stand mixer fitted with a dough hook* or a large mixing bowl, combine warm water and brown sugar. Sprinkle yeast on top and let sit for 5 minutes until foamy. If the yeast does not foam, it is dead and you will need to start over with fresh yeast.
Add flour, pumpkin purée, pumpkin pie spice, and salt and mix on low until combined. Increase speed to medium and mix, scraping down the sides of the bowl, until no dry spots remain.This will be a very wet, sticky dough that you could not knead if you tried.
Transfer the dough to a large, oiled bowl and cover with plastic wrap. Let rise for 2-3 hours, until doubled in size.
Brush a 9x13-inch pan with 2 Tablespoons melted butter and set aside**.
Once the dough has risen, use a spatula to scrape around the perimeter of the bowl, deflating the dough. Transfer the dough to the center of the prepared 9x13-inch pan. Dip your fingers in the melted butter (or you can get the lightly wet), then use your fingers to lightly press the dough until it reaches the edges of the pan (this is not the dimpling step yet!). Cover with plastic wrap or a clean kitchen towel and let rise 1 ½-2 hours, until doubled in size and the dough fills (or nearly fills) the pan.
Near the end of the rise, preheat the oven to 450°F and make the topping. Melt the butter in a small saucepan over low heat. Remove from heat and stir in the brown sugar and cinnamon.
Drizzle the topping evenly over the dough. With wet fingers (you can just dip your fingers in the topping), press deep dimples all over the dough. If you find the dough is sticking to your fingers, you can get them slightly wet, then try again. After dimpling, the dough will look a bit messy!
Bake for 25-30 minutes, until the focaccia is golden and crusty. Let cool for 10 minutes in the pan, then transfer to a cooling rack to cool fully.
While the focaccia cools, combine confectioner's sugar, milk and vanilla extract in a small bowl. Whisk until smooth and combined. If you want a thinner frosting, add more milk. Drizzle the frosting over the cooled focaccia, slice and serve!
Video
Notes
*You do not need a stand mixer to make this recipe. You can also make the dough in a large mixing bowl and mix with a wooden spoon.
** If doubling or tripling this recipe, bake each focaccia in its own 9x13-inch pan (instead of a larger pan).
To make this recipe with active sourdough starter, omit the yeast and replace the sourdough discard with active starter (200g). You will also need to increase the rise times.