Preheat your oven to 350 degrees F. Grease a 9×13 inch cake pan with nonstick spray or rub with butter.
Make the streusel: In a large bowl, whisk together 3 cups flour, 1 cup brown sugar, ½ cup granulated sugar, 1 teaspoon kosher salt, 1 tablespoon cinnamon, and 1 tablespoon pumpkin pie spice.
Melt 1 cup butter in a medium bowl in the microwave. Pour into the larger bowl and stir the butter into the flour.
Set aside the streusel mixture, ideally refrigerate it if you have room.
For the cake: In a large bowl or stand mixer, whisk together 2 and ¼ cups flour, 1 and ½ cups granulated sugar, 1 tablespoon baking powder, ¾ teaspoon baking soda, ¾ teaspoon kosher salt, 1 tablespoon pumpkin pie spice, and 1 teaspoon cinnamon.
Chop ½ cup softened butter into chunks and add it to the flour mixture.
Use a spatula to scoop out half of the can of pumpkin puree and add it to the bowl with the flour and butter. Blend until moistened.
In the bowl where the butter was melted, whisk together the remaining pumpkin, 4 eggs, ¼ cup vegetable oil, and 1 tablespoon vanilla.
Add the egg mixture to the flour mixture in 3 additions, beating well between each addition.
Spread 2 cups of batter into the bottom of the prepared cake pan.
Sprinkle 1 cup of streusel evenly over the top.
Spread another 2 cups batter on top and evenly distribute.
Add another 1 cup streusel on top.
Add the remaining batter and spread evenly.
Spread another 2 cups of streusel on top of the cake.
Bake the cake at 350 for 35 minutes.
Quickly add the remaining streusel on top of the cake, focusing on areas where the cake has puffed.
Bake for another 10-15 minutes. The cake is done when a toothpick inserted in the center comes out clean.
Let the cake cool on a wire rack for at least 15-20 minutes before cutting.
Make the icing: In a medium bowl, beat the softened butter until smooth.
Mix in vanilla, kosher salt, milk, and powdered sugar, adjusting milk to reach desired consistency.
Drizzle the icing over the cake.
Serve warm; reheating individual servings in the microwave if desired.