Preheat the oven to 350 degrees Fahrenheit. Grease a 9x9-inch baking dish.
In a large mixing bowl, sift the flour, baking powder, baking soda, salt, and pumpkin pie spice.
Whisk together pumpkin puree, sugars, milk, and vanilla extract in a separate bowl until smooth.
Pour the wet mixture into the dry ingredients and mix until just combined. The batter will be thick.
Make the crumb topping. Whisk the flour, brown sugar, cinnamon, and melted butter until the mixture clumps together and forms crumbs.
Spoon the cake batter into the prepared baking dish and spread evenly. Sprinkle with the crumb topping.
Bake it for 30-35 minutes, or until a toothpick inserted into the center comes out clean or with a few crumbs attached.
Make the vanilla glaze. Whisk together the powdered sugar, ½ tablespoon of milk, and vanilla in a bowl. Add more milk if necessary to achieve a drizzly consistency.
Drizzle the vanilla glaze over the slightly cooled cake.
