In a mixing bowl, whisk together the brown sugar, flour, pumpkin pie spice, cinnamon, and salt.
¼ cup light brown sugar, ⅔ cup all-purpose flour, 1 teaspoon pumpkin pie spice, ½ teaspoon ground cinnamon, Pinch of salt
Add the cold butter. Using your hands or a pastry cutter, combine the mixture until it forms a shaggy texture with no visible flour streaks.
5 tablespoons unsalted butter
Set aside. This topping can be made ahead of time and stored in an airtight container for up to 5 days.
Prepare the Cake:
Preheat your oven to 350°F. Spray the bottom of an 8x8 metal pan, line with parchment paper, and spray again. If needed, use metal binder clips to hold down the sides of the parchment paper.
In a medium-sized bowl, whisk together the flour, baking powder, pumpkin pie spice, cardamom, cinnamon, ginger, nutmeg, and salt until well combined. Set aside.
1 ½ cups all-purpose flour, 1 tablespoon baking powder, ½ teaspoon pumpkin pie spice
In the bowl of an electric stand mixer fitted with the paddle attachment, cream together the granulated sugar, brown sugar, and eggs on medium speed until light and fluffy, about 5 minutes.
⅔ cup granulated sugar, ½ cup light brown sugar, 3 large eggs, ¼ teaspoon ground cardamom, 1 ½ teaspoons ground cinnamon, ½ teaspoon ground ginger, ¼ teaspoon ground nutmeg, ¾ teaspoon salt
Add the vegetable oil and vanilla extract, and beat on medium speed until fully incorporated, about 30 seconds.
½ cup vegetable oil, 1 teaspoon pure vanilla extract
Add the pumpkin purée and mix on low speed until combined, about 30 seconds more.
1 cup pumpkin purée
With the mixer on the lowest speed, gradually add the dry ingredients to the pumpkin mixture, mixing until just combined.
Assemble and Bake:
Pour the pumpkin batter into the prepared 8x8 pan. Use the back of a spoon to smooth the batter evenly.
Evenly sprinkle the cinnamon topping over the pumpkin cake batter.
Bake for 35-38 minutes, or until a toothpick inserted into the center comes out with just a few moist crumbs.
Let the cake cool completely in the pan.
Finish and Serve:
When ready to serve, mix 1 cup of powdered sugar with 3 tablespoons of milk to create a glaze. Drizzle over the cooled cake.