Preheat the oven to 350°F (175°C). Line a 9-inch square baking pan with parchment paper, leaving some overhang on the sides for easy removal.
Prepare the crumb topping first. Whisk the flour, brown sugar, cinnamon, and salt together in a medium bowl. Add the cold cubed butter and work it into the dry ingredients with a pastry cutter or fork until large, irregular crumbs form. Set aside.
For the cake batter, whisk together the flour, baking soda, baking powder, salt, cinnamon, nutmeg, ginger, and cloves in a large bowl.
In a separate bowl, whisk the pumpkin puree, brown sugar, vegetable oil, maple syrup, milk, and vanilla extract until smooth and well combined.
Pour the wet mixture into the dry ingredients. Using a rubber spatula, gently fold everything together just until no dry streaks remain. The batter will be thick, so avoid overmixing.
Transfer the batter to the prepared baking pan and spread it into an even layer.
Scatter the crumb topping evenly over the entire surface, gently pressing some of the larger crumbs into the batter so they stay in place while baking.
Bake for 30–35 minutes, checking at the 30-minute mark. The cake is ready when a toothpick inserted into the center comes out clean or with a few moist crumbs attached. Avoid overbaking, as this can dry out the pumpkin cake.
Remove the cake from the oven and let it cool in the pan for about 15–20 minutes. Transfer it to a wire rack if you want it to cool completely before glazing.
While the cake cools, make the vanilla glaze. Whisk the confectioners’ sugar, milk, vanilla extract, and salt together in a small bowl until smooth. Add a few extra drops of milk if the glaze is too thick, or a little more confectioners’ sugar if it is too thin.
Drizzle the glaze over the warm or cooled coffee cake. Slice into 9 squares and serve.