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. (save the bowl)
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. Add the chopped butter to the flour mixture.
Use a spatula to scoop half the can of pumpkin puree and add it to the flour and butter, then blend.
In the same medium bowl that you melted butter in, add all the remaining pumpkin from the can. Whisk in 4 eggs, ¼ cup vegetable oil, and 1 tablespoon vanilla. Beat well until the eggs are well blended.
Add the egg mixture to the flour mixture in 3 additions, beating for about 20 seconds after each one.
Spread 2 cups of batter into the bottom of your prepared cake pan. Sprinkle 1 cup of streusel evenly over the top.
Spread another 2 cups batter on top, then add another 1 cup streusel on top, and the rest of the batter.
Spread another 2 cups of streusel on top of the cake. Bake the cake at 350 for 35 minutes.
Remove the cake from the oven and sprinkle all the remaining streusel on top. Bake for another 10-15 minutes.
Let the cake cool on a wire rack for at least 15-20 minutes before cutting into it.
Make the icing: In a medium bowl, beat ¼ cup butter until smooth, then add 1 teaspoon vanilla, ½ teaspoon kosher salt, 3 tablespoons milk, and 2 cups powdered sugar. Beat until very smooth.
Drizzle the icing over the cake.
The cake is best served warm! Zap individual servings in the microwave for 10-20 seconds.
This cake will keep well covered on the counter for 2-3 days. After that, put it in the fridge.