In a medium bowl, whisk together the all-purpose flour, brown sugar, granulated sugar, salt, cinnamon, and pumpkin pie spice until well combined. Add melted butter and mix until it resembles wet sand. Refrigerate for 30 minutes.

In a large mixing bowl, combine the flour, granulated sugar, baking powder, baking soda, cinnamon, and pumpkin pie spice. Cut in the softened butter until it resembles coarse crumbs. Gently fold in the pumpkin puree.

In a separate bowl, whisk together remaining pumpkin puree, eggs, vegetable oil, and vanilla extract until blended. Gradually pour wet mixture into dry ingredients, stirring until just incorporated.

Preheat your oven to 350°F (175°C) and grease a 9x13-inch baking pan. Spread half of the batter in the prepared pan, sprinkle with a layer of streusel, then add remaining batter and top with leftover streusel.

Place cake in the oven and bake for 35 minutes. Sprinkle remaining streusel on top and bake for an additional 10-15 minutes until a toothpick comes out clean.

Let the cake cool in the pan on a wire rack for at least 20 minutes. Whisk together the powdered sugar, milk, vanilla extract, and a pinch of salt to make the glaze. Drizzle over the cooled cake before slicing.