Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper and set it aside.
Make the streusel: In a mixing bowl, combine the brown sugar, pumpkin spice, and flour. Use a fork to mix them together. Add the softened butter and blend it into the dry ingredients until a crumbly mixture forms. Set aside.
Place the pumpkin puree on a paper towel and squeeze out any excess moisture. Transfer the drained puree to a large mixing bowl.
Add the browned butter, white sugar, and brown sugar to the bowl with the pumpkin puree. Stir until well combined.
Separate the egg yolks and add them to the mixture, along with the vanilla extract. Whisk until smooth.
Sift the dry ingredients (flour, baking soda, baking powder, salt, and pumpkin spice) into the wet mixture. Use a rubber spatula to fold everything together until a thick dough forms.
Use a 2-inch scooper to portion the dough into balls, placing them on the prepared baking sheet about 2 inches apart.
Gently press down each dough ball with your fingers, creating a small well in the center.
Fill each well with the prepared pumpkin streusel.
Bake for 12 minutes or until the cookies are slightly browned around the edges.
Remove from the oven and let the cookies cool while you make the glaze.
To make the glaze: In a small bowl, whisk together powdered sugar, vanilla extract, and milk. Start slowly to dissolve the sugar, then whisk more vigorously to remove any clumps, creating a smooth glaze.
Drizzle the glaze over the slightly cooled cookies.