Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking pan.

In a mixing bowl, whisk together the all-purpose flour, brown sugar, granulated sugar, kosher salt, cinnamon, and pumpkin pie spice. Drizzle in the melted butter and mix until crumbly. Refrigerate the streusel mixture.

In a separate bowl, whisk together the all-purpose flour, remaining sugars, baking powder, baking soda, and a pinch of salt. Add the softened butter and half of the pumpkin puree, mixing until crumbly.

Mix the remaining pumpkin puree, eggs, vegetable oil, and vanilla extract in another bowl. Gradually pour into the dry ingredients, folding gently until just combined.

Spread half the batter into the prepared pan, smooth the top, and sprinkle with streusel. Repeat with remaining batter and streusel.

Bake for 35 minutes, add remaining streusel on top, and bake for an additional 10-15 minutes or until a toothpick comes out clean.

Allow the cake to cool in the pan for at least 15-20 minutes.

In a small bowl, combine softened butter, vanilla extract, a pinch of salt, milk, and powdered sugar to make icing. Drizzle over cake once cooled.