In a small bowl, mix flour, both sugars, and cinnamon. Stir in melted butter until crumbs form. Place in the fridge while you make the cookie dough.
In a small saucepan, melt the butter over medium heat, stirring often, until golden brown with a nutty aroma. Pour into a heatproof bowl and let it cool for 10–15 minutes.
In a large bowl, whisk together the browned butter and brown sugar until smooth.
Add the blotted pumpkin purée, egg yolk, and vanilla, mixing until combined.
In a separate bowl, whisk together flour, baking soda, baking powder, cinnamon, nutmeg, cloves, and salt.
Fold dry ingredients into wet ingredients until just combined. The dough will be soft but not overly sticky.
Assemble the cookies: Preheat oven to 350°F (175°C) and line two baking sheets with parchment paper. Scoop about 2 tablespoons of dough per cookie, roll into balls, and place 2 inches apart on the baking sheets. Gently press down the tops of each dough ball, then sprinkle with crumb topping, pressing lightly so it sticks.
Bake: Bake for 11–13 minutes, until edges are set and the centers look slightly soft. Let cookies cool on the baking sheet for 5 minutes before transferring to a wire rack.
Whisk together powdered sugar, milk, and vanilla until smooth. Drizzle over cooled cookies.
