In a mixing bowl, combine ½ cup softened unsalted butter and ½ cup brown sugar. Stir in 1 cup all-purpose flour, 1 teaspoon pumpkin pie spice, and a pinch of salt. Mix until large crumbs form, resembling a coarse texture. Chill the streusel in the refrigerator for at least 30 minutes.

Spread ½ cup of canned pumpkin puree on a plate, ensuring it sits flat. Press down gently with a paper towel to absorb excess moisture until nearly dry.

In a small bowl, whisk together 1½ cups all-purpose flour, 1 teaspoon pumpkin pie spice, ½ teaspoon baking soda, ½ teaspoon baking powder, and ¼ teaspoon salt.

In a large mixing bowl, beat together ½ cup softened unsalted butter and 1 cup packed brown sugar until light and fluffy. Add 2 egg yolks and 1 teaspoon vanilla extract, mixing until pale and creamy.

Fold in the prepared pumpkin puree, then slowly add the dry ingredient mixture, stirring just until combined.

Scoop out tablespoon-sized balls of dough and place them onto prepared baking sheets. Indent the tops lightly and sprinkle the chilled streusel topping over each cookie.

Preheat your oven to 350°F (175°C) and bake the cookies for 11-12 minutes, until set and slightly golden around the edges.

Let the cookies rest on the baking sheet for about 10 minutes, then transfer to a wire rack to cool completely.

Whisk together 1 cup powdered sugar and 1 teaspoon vanilla extract, adding just enough milk to reach a drizzle-able consistency. Drizzle over cooled cookies.