Preheat oven to 350°F (175°C) and line two baking sheets with parchment paper.

In a medium bowl, whisk together the flour, pumpkin pie spice, cinnamon, baking soda, and salt until well combined.

In a large bowl, cream together butter, brown sugar, and granulated sugar using an electric mixer until light and fluffy (about 2-3 minutes).

Add the egg and vanilla extract, beating until smooth.

Mix in the pumpkin puree until just combined (mixture may look slightly curdled).

Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined.

If the dough is too sticky, chill for 30 minutes.

In a small bowl, mix flour, brown sugar, cinnamon, and salt.

Cut in the cold butter using a pastry cutter or fork until the mixture forms coarse crumbs.

Stir in chopped nuts if using.

Use a 2-tablespoon scoop to drop cookie dough onto the prepared baking sheets.

Flatten the tops slightly and sprinkle a generous amount of streusel topping onto each.

Bake for 11-13 minutes until the edges are set but centers remain soft.

Let cookies cool on the baking sheet for 5 minutes, then transfer to a wire rack.

In a small bowl, whisk together powdered sugar, milk, vanilla, and salt until smooth.

Drizzle over completely cooled cookies and let set for 20 minutes.