First, remove the moisture from the pumpkin puree. Spread the pumpkin puree in a thin layer on several layers of paper towels. Use additional paper towels to blot the pumpkin puree until most of the moisture is removed and the pumpkin puree is dry. The pumpkin puree will reduce by half, so you should have ⅓ cup of pumpkin puree remaining. Set aside.
Preheat the oven to 350℉ (177℃). Line baking sheet pans with silicone baking mats or parchment paper.
In a medium mixing bowl, whisk together the all-purpose flour, pumpkin pie spice, baking soda, and salt. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment or in a large mixing bowl with an electric hand mixer, mix together the melted unsalted butter, light brown sugar, and granulated sugar until well combined. Add in the dried pumpkin puree, egg, egg yolk, and vanilla extract, and mix until combined and smooth. Add in the flour mixture and mix on low speed until the cookie dough forms. Set aside.
Next, make the cinnamon streusel topping. In the bowl of a stand mixer fitted with a paddle attachment or in a medium mixing bowl with an electric hand mixer, cream the softened unsalted butter and light brown sugar until smooth. Add the all-purpose flour and ground cinnamon and mix on low speed until the mixture resembles large crumbs.
Portion the pumpkin cookie dough using a large cookie scoop (3 tablespoons). Place the cookie dough balls on the prepared baking sheet pans, allowing room for spreading. Use the back of a spoon to gently press into the center of the cookies to create an indentation. Add 1 to 2 tablespoons of the streusel topping to the center of the cookie.
Bake the cookies for 12 to 13 minutes, until the edges are set and the centers are slightly underbaked. Cool the cookies on the pan for 2 minutes and then transfer to a wire rack to cool completely.
To make the vanilla glaze, stir together the powdered sugar, milk, and vanilla extract. Use a spoon to drizzle the vanilla glaze over the cooled cookies.