Brown the butter in a saucepan over medium heat until fragrant and golden brown. Pour into a bowl to cool until lukewarm.

Blot the pumpkin puree on paper towels to remove excess moisture; set aside.

In a large bowl, whisk together the flour, pumpkin spice, baking soda, and salt.

In another bowl, stir the cooled brown butter with brown sugar and maple syrup until combined. Add egg yolk, vanilla extract, pumpkin, and optional maple extract. Mix until smooth.

Gradually stir in the dry ingredients until just combined to form a slightly sticky dough.

Mix granulated sugar and spice in a shallow bowl. Use a cookie scoop or spoon to portion dough (≈1 Tbsp), roll into balls, then coat in spiced sugar mixture.

Place on parchment‑lined baking sheets about 2 inches apart. Chill trays for best shape, or bake immediately.

Bake at 350 °F (175 °C) for 12 minutes, until edges set but centers remain soft. Let cool on sheets briefly, then transfer to wire racks.

If glazing, once cookies are cooled, whisk powdered sugar, maple syrup, and milk until smooth. Drizzle over cookies and allow to set.