Preheat the oven to 350°F. Grease a 9" cast iron skillet with butter and set aside.

In a large mixing bowl, stir together the flour, sugar, baking powder, baking soda, and salt.

In a medium bowl, add milk, ½ cup melted butter, pumpkin puree, egg, and vanilla extract. Stir to combine.

Pour the wet ingredients into the dry ingredients and mix well to incorporate.

Pour cake batter into the prepared skillet and use a spatula to create a smooth even layer.

In a small bowl, add ½ cup melted butter, brown sugar, and pumpkin pie spice. Stir to combine.

Pour the crumb topping over the cake.

Use a butter knife to swirl the mixture into the cake batter.

Bake in a preheated oven for 27-30 minutes or until a toothpick inserted into the center comes out clean.

Allow the cake to cool for 10 minutes.

Add powdered sugar, milk, vanilla extract, and ¼ teaspoon pumpkin pie spice to a small bowl. Stir to combine.

Spoon the icing onto the cake.

Slice and serve.