Make the crumb topping: In a bowl, combine 1 cup flour, 1/2 cup brown sugar, and 1 1/2 teaspoons cinnamon. Cut in the cold cubed butter with your fingers until it forms pea-sized clumps, then chill in the fridge while you make the batter.
Preheat and prep pan: Preheat the oven to 350°F. Grease a 9-inch square baking pan and line it with parchment paper, leaving an overhang for easy removal.
Mix wet ingredients: In a large bowl, whisk together the pumpkin puree, brown sugar, eggs, melted butter, and sour cream until smooth and well combined.
Combine dry ingredients: In a separate bowl, whisk the flour, baking powder, baking soda, salt, and pumpkin pie spice together until evenly distributed.
Fold batter together: Add the dry ingredients to the wet ingredients and fold gently just until no streaks of flour remain. Avoid overmixing, which can make the cake dense.
Pour batter into pan: Pour the batter into the prepared pan and spread it evenly with a spatula, smoothing the top.
Add crumb topping: Remove the chilled crumb mixture from the fridge and scatter it evenly over the batter, pressing lightly so the crumbs adhere.
Bake the cake: Bake at 350°F for 40 to 45 minutes, until a toothpick inserted in the center comes out clean and the crumb topping is golden brown.
Cool before slicing: Let the cake cool in the pan for at least 20 minutes before lifting it out using the parchment overhang. Slice into 9 squares and serve.