Preheat oven to 350°F and lightly grease an 8x8 baking dish.
Whisk pumpkin puree, brown sugar, melted butter, eggs, and vanilla in a mixing bowl until smooth.
Combine flour, baking powder, baking soda, salt, cinnamon, nutmeg, and cloves in a separate bowl.
Add dry ingredients to wet ingredients and stir just until combined, creating a thick batter.
Spread batter evenly into the prepared baking dish.
Mix flour, brown sugar, and cinnamon in a small bowl for the crumble topping.
Cut in cold butter with a fork until the mixture forms coarse crumbs.
Sprinkle crumble evenly over the batter.
Bake for 35 to 40 minutes, or until a toothpick inserted in the center comes out clean or with soft crumbs.
Cool the cake in the pan for at least 20 minutes.
Stir powdered sugar, milk, and vanilla to make a smooth icing.
Drizzle icing over the cooled cake.
Slice and serve warm or at room temperature.