Preheat oven to 350°F. Whisk together the flour, baking powder, salt, cinnamon and pumpkin spice for the cake and set aside.
In a separate medium bowl, cream the butter and brown and white sugars until creamy and fluffy. Add in the egg, milk and vanilla and beat until incorporated. Add in the pumpkin and mix until combined.
Slowly add in the dry ingredients and beat only until combined. Try not to over mix the batter at this point. Spread the batter evenly into a well greased 9x9 inch baking pan.
Make the streusel topping: Mix the brown sugar, flour and cinnamon to combine. Add the cubed butter. Using a fork or pastry cutter, or fingers, break down the butter until small and crumbly, allowing the flour mixture to coat the little pieces of butter.
Sprinkle the streusel over the coffee cake batter evenly. Bake for about 27-32 minutes or until the crumble topping is golden brown and a toothpick comes out of the center clean.
Allow to cool for about 10 minutes before adding the icing. Whisk the icing ingredients together, adjusting the milk to desired thickness. Drizzle over top. Serve still warm, or at room temperature.
Store in an air tight container at room temperature for about 2-3 days or refrigerated for about 5-7 days.