Blot the pumpkin: Line a medium bowl with several paper towels. Place the pumpkin puree in the bowl. Using another paper towel, press down to blot excess moisture out of the pumpkin. Repeat with new paper towels until the pumpkin feels much drier and has been reduced by half, to 1/2 cup (113g). Set aside.

In a medium bowl, whisk together the flour, baking soda, pumpkin pie spice, cinnamon, and salt. Set aside.

In a large bowl, whisk together the melted butter, granulated sugar, brown sugar, and maple syrup until combined. Whisk in the egg yolk and vanilla extract until incorporated, then whisk in the 1/2 cup of blotted pumpkin. Pour the dry ingredients into the wet ingredients and stir with a silicone spatula or wooden spoon until combined. The cookie dough will be very soft.

Cover tightly and refrigerate the cookie dough for at least 2 hours or up to 3 days.

Meanwhile, in a small bowl, whisk together the flour, brown sugar, and pumpkin pie spice. Using a fork or a handheld mixer on low speed, mix in the butter until sandy and crumbly. Feel free to work the mixture together with your hands if it’s not coming together. Place the topping in the refrigerator or freezer until needed in step 7.

Preheat the oven to 350°F (177°C). Line large baking sheets with parchment paper or silicone baking mats.

Scoop and roll the chilled cookie dough into balls, about 1.5 Tbsp (35g) of dough each, and arrange 3 inches apart on the prepared baking sheets. Use your thumb to press a few indents into the middle of each cookie, to make a shallow bowl shape. Sprinkle a generous amount of the cold crumb topping on top of each cookie.

Bake for 14–15 minutes or until the edges of the cookies are lightly browned and set. Cool the cookies on the baking sheet for 10 minutes, then transfer them to a cooling rack.

In a small saucepan over low heat, melt the butter and maple syrup together, whisking occasionally. Once the butter has melted, remove from heat and whisk in the sifted confectioners’ sugar. Taste. Add a pinch of salt, if desired. Drizzle over cookies. Icing will set after about 1 hour.

Store cookies in an airtight container at room temperature for up to 4 days, or in the refrigerator for up to 1 week.