In a small bowl, add milk and icing sugar.
Add the vanilla extract.
whisk until smooth.
In a separate bowl, combine the brown sugar, all-purpose flour, pumpkin pie spice, salt, and softened butter.
Mix until crumbly and evenly combined. Set aside.
In a large mixing bowl, whisk together the all-purpose flour, pumpkin pie spice, baking powder, baking soda, and salt.
In another bowl, Add the softened butter and light brown sugar.
Mix until smooth and well combined.
Add the pumpkin purée, egg yolks, and vanilla extract.
Mix until well combined.
Gradually add the prepared dry ingredients to the wet mixture.
Fold everything together with a rubber spatula until a soft, smooth cookie dough forms with no dry flour remaining.
Scoop portions of dough onto a parchment-lined baking sheet.
Sprinkle the prepared streusel evenly over each cookie dough portion and gently press it into the tops.
Bake in a preheated 350°F (175°C) oven for 10–12 minutes, or until the cookies are lightly golden around the edges.
Let the cookies cool on the baking sheet for 5 minutes, then transfer them to a wire rack.
Drizzle the cooled cookies with the prepared vanilla glaze.
Allow the glaze to set for a few minutes before serving.