1. Brown the Butter: Melt the butter in a saucepan over medium-low heat. Once melted, increase the heat to medium and let the butter foam and sizzle, stirring continuously, until it begins to brown and emit a nutty aroma (about 2-3 minutes). Pour the browned butter into a medium mixing bowl and let it cool completely.

2. Mix the Wet Ingredients: In the cooled browned butter, whisk in the light brown sugar, white sugar, maple syrup, egg yolk, vanilla extract, and pumpkin puree until the mixture is smooth and well combined.

3. Combine the Dry Ingredients: In a separate bowl, whisk together the all-purpose flour, baking powder, baking soda, salt, pumpkin pie spice, and ground cinnamon.

4. Form the Dough: Gradually fold the dry ingredients into the wet mixture until a dough forms. Cover the bowl with plastic wrap and refrigerate the dough for 30 minutes to allow the flavors to meld and the dough to firm up.

5. Prepare for Baking: Preheat your oven to 350°F and line baking sheets with parchment paper. In a small bowl, combine the remaining 1/2 cup of white sugar and 1/2 tablespoon of pumpkin pie spice for the rolling mixture.

6. Shape and Bake the Cookies: Scoop the chilled dough into 1-inch balls, roll them in the sugar-spice mixture, and place them on the prepared baking sheets, spacing them about 2 inches apart. Bake for 10-12 minutes, or until the edges are set and the tops are slightly cracked. Let the cookies cool on the baking sheets for 5 minutes before transferring them to wire racks to cool completely.