Slice the unsalted butter into even pieces and place them in a light-colored saucepan over medium-low heat. Whisk steadily as the butter melts so it heats gently and does not burn.

Continue whisking as the butter foams and bubbles. When the foam begins to settle, the butter smells nutty and rich, and amber milk solids form on the bottom of the pan, it is properly browned.

Take the pan off the heat right away and pour the browned butter, including all the browned bits, into a heat-safe glass bowl. Use a rubber spatula to scrape every last speck from the pan into the bowl.

Refrigerate the bowl for 20 to 30 minutes, stirring the butter every 10 minutes, until it is cool but still completely liquid.

Do not let the butter solidify. It should remain pourable and simply reach room temperature so it blends smoothly into the cookie dough.

Lay a few layers of paper towels on a plate and spread the pumpkin puree over them in a thin, even layer. Place more paper towels on top and press gently to soak up the extra moisture.

After blotting, the puree will be noticeably reduced in volume, which helps keep the cookies chewy rather than cakey.

Scrape the pressed pumpkin puree into a small bowl with a rubber spatula and set it aside.

Put the cooled browned butter in a large mixing bowl, add the granulated sugar and dark brown sugar, and stir with a rubber spatula until the mixture is smooth and no butter streaks remain.

Add the blotted pumpkin puree, egg yolk, and vanilla bean paste, and mix until everything is fully combined into a glossy wet mixture.

In a separate medium bowl, whisk together the all-purpose flour, pumpkin pie spice, baking soda, cream of tartar, salt, and ground ginger.

Fold the dry ingredients into the wet ingredients with the rubber spatula, mixing just until combined. Avoid overmixing so the cookies stay tender.

Cover the mixing bowl tightly with plastic wrap and refrigerate the dough for 30 minutes, or until it is firm enough to scoop.

Just before taking the dough out of the refrigerator, prepare the coating so it is ready to use.

In a medium bowl, whisk together the granulated sugar, pumpkin pie spice, and cinnamon until evenly combined, then set the bowl aside.

Line a baking sheet with parchment paper and set it near your work area.

Using a #40 cookie scoop, which holds about 2 tablespoons, scoop chilled dough balls onto the baking sheet. The dough will be sticky.

Roll each dough ball in the cinnamon sugar mixture until lightly coated, then place it back on the prepared baking sheet.

After filling one baking sheet, return the remaining cookie dough to the refrigerator while you bake the first batch.

Bake at 350 degrees F for 10 to 12 minutes, just until the edges begin to brown. The cookies will look slightly puffed and a touch underdone in the center, but they will set as they cool.

Take the pan out of the oven and let the cookies rest on the baking sheet for about 5 minutes.

While the cookies are still warm, sprinkle them lightly with flaky sea salt if desired. After 5 minutes, transfer the cookies to a wire rack to cool completely.