Brown the butter first. Add the butter to a light-colored saucepan over medium heat. Stir occasionally and watch closely. After about 5 to 7 minutes the butter will foam, then the foam will subside and you will see golden-brown specks form on the bottom of the pan. It should smell nutty and toasty, not burned. Pour it immediately into a large mixing bowl and let it cool for 20 minutes. Do not skip the cooling step or the heat will scramble your egg.

Pat the pumpkin puree dry. Spread it on two or three layers of paper towels, press another layer on top, and press firmly. Repeat until the towels no longer look wet. You want to remove as much moisture as possible so the cookies stay chewy and not cakey.

Make the dough. Once the brown butter has cooled, add 1 cup granulated sugar and the brown sugar to the bowl and beat with a hand mixer on medium for about 1 minute. Mix in the dried pumpkin puree, egg yolk, and vanilla until smooth. In a separate bowl, whisk together the flour, baking soda, cream of tartar, salt, cinnamon, ginger, and nutmeg. Add the dry ingredients to the wet and stir with a spatula until just combined. The dough will be soft.

Chill the dough. Cover the bowl tightly with plastic wrap and refrigerate for at least 30 minutes, and up to 48 hours. Chilling firms the fat back up so the cookies bake thick and hold their shape without spreading flat.

Preheat your oven to 350 degrees F. Line two baking sheets with parchment paper. In a small bowl, stir together the 2 tablespoons sugar and 1 1/2 teaspoons cinnamon for rolling.

Scoop and roll. Scoop the chilled dough into balls about 1 1/2 tablespoons each. Roll each ball between your palms until smooth, then roll generously in the cinnamon-sugar mixture to coat all sides. Place on the prepared baking sheets about 2 inches apart.

Bake for 11 to 13 minutes, until the edges look set and the tops have a slightly crackled appearance. The centers will still look just barely underdone, which is exactly right. They finish setting as they cool on the pan. Let the cookies rest on the baking sheet for 5 minutes before transferring to a wire rack.