First, preheat the oven to 350-degrees, and lightly spray or grease an 8-inch square cake pan.
Then, make the streusel: combine the brown sugar, flour, oats, pumpkin pie spice, and salt in a bowl. Mix well. Add the diced butter, and mix using two forks or your fingertips until combined into a crumbly mixture.
Next, make the cake: whisk together the flour, baking soda, baking powder, salt, pumpkin pie spice, granulated sugar and brown sugar.
In a separate bowl, whisk together the pumpkin, melted butter, milk, egg, and vanilla.
Add the pumpkin mixture to the flour mixture, and stir until no lumps remain.
Pour half of the cake batter in the pan, and sprinkle half of the the streusel on top.
Spread the remaining pumpkin batter on top (it’s okay if it’s not perfect).
Bake on the center rack for 34-37 minutes, until a toothpick tester come out with only moist crumbs. The cake will start to pull away from the edge of the pan, too.
Let cool slightly, and then slice up and serve.