Preheat your oven to 350°F (175°C). Grease a 9×9-inch baking pan with butter or line it with parchment paper for easy removal.
In a small bowl, whisk together the flour, brown sugar, and cinnamon. Add the cold, cubed butter and use a pastry cutter or your fingers to work the butter into the dry ingredients until the mixture resembles coarse crumbs. Set this aside in the refrigerator.
In a medium bowl, whisk together the 2 cups of flour, baking soda, baking powder, salt, and pumpkin pie spice. Ensure there are no lumps of spices left in the mixture.
In a large mixing bowl, beat the softened butter and granulated sugar together until the mixture is light and fluffy. This should take about 2 to 3 minutes using an electric mixer.
Add the eggs one at a time, beating well after each addition. Mix in the pumpkin puree, sour cream, and vanilla extract until the mixture is smooth and well combined.
Gradually add the dry flour mixture to the wet ingredients. Fold them in gently using a spatula or mix on low speed just until combined. Do not overmix, as this can make the cake tough.
Spread the batter evenly into the prepared baking pan. Sprinkle the chilled streusel topping over the entire surface of the batter. Bake for 40 to 45 minutes, or until a toothpick inserted into the center comes out clean.
Remove the pan from the oven and place it on a wire rack to cool for at least 15 minutes before slicing. This allows the structure to set and the flavors to meld.