Brown the 1 cup unsalted butter: In a pan set over medium heat, melt the butter, swirling the pan often, until it melts and gives off a slight nutty aroma. Remove from the heat and transfer to a large bowl.
Preheat the oven to 350℉ and butter and line a 9x13-inch baking pan. Add the ¾ cup brown sugar, ½ cup granulated sugar, 2 large eggs, ½ cup pure pumpkin puree, 2 cups oat flour, ½ cup almond flour, 1 teaspoon baking powder, 1 teaspoon ground cinnamon, ½ teaspoon ground ginger, ½ teaspoon ground nutmeg, and ¼ teaspoon fine sea salt to the browned butter and stir well to form a smooth batter.
Pour the batter into the prepared pan and rest for 15 minutes. Bake the pumpkin squares for 35-45 minutes, checking for doneness around 30 minutes. The squares will be less soft the longer they bake.
Let cool in the pan set on a rack for 20 minutes, then cut into squares.
Notes
About that bake time ... I prefer a more cake-like final result, so I tend to bake these squares a bit longer. However, if you love a gooier dessert, you can cut the baking time a bit. Check around 30 minutes and keep baking until they reach your desired texture.
Cool to set the squares. This is especially important if you underbake the squares a little bit. The squares will set as they cool, so while it's tempting to cut right into them, hold off! (This goes for gluten-free AND non-gluten-free bakes by the way.)
Make it dairy-free. Use a non-dairy butter of your choice instead of regular butter to make this dairy-free.
Can I swap flours? Yes, you can easily use another gluten-free flour, such as brown rice flour, sorghum flour, 1:1 gluten-free flour, or a homemade gluten free flour blend.
Make it refined sugar-free. An easy way to make this recipe with unrefined sugar is to swap coconut sugar for the brown sugar and maple syrup for the granulated sugar.