Brown the butter by melting it in a light-colored skillet until it becomes foamy and the milk solids are brown. Transfer to a glass bowl and cool in the refrigerator or freezer.

Cook the pumpkin puree in a small saucepan over medium heat for 10 to 15 minutes until thick. Transfer to a bowl and cool to room temperature.

Preheat the oven to 350?F. Line baking sheets with silicone baking mats or parchment paper.

In a large mixing bowl, beat the cooled brown butter, brown sugar, and granulated sugar with an electric handheld mixer for 3 to 4 minutes until light and creamy. Add the egg, egg yolk, and vanilla and beat until combined.

Add the flour, cinnamon, baking soda, salt, allspice, nutmeg, cloves, and cardamom and beat until no dry flour is visible. Fold in the chopped chocolate.

Use a 1.5 tablespoon cookie scoop to portion out dough balls on lined cookie sheets about 2 inches apart. Press the remaining chocolate into the tops of each cookie.

Bake in batches for 10 to 12 minutes until edges are golden brown and centers appear slightly underbaked. Sprinkle flaky salt on top.

Allow cookies to cool on the baking sheet for 5 minutes, then transfer to a cooling rack to cool completely.