Brown the butter by melting it in a light-colored skillet over medium heat, stirring constantly until it becomes foamy and the milk solids brown, then transfer to a glass bowl and cool.

Cook the pumpkin puree in a small saucepan over medium heat for 10 to 15 minutes, stirring regularly to remove excess moisture, then cool to room temperature.

Preheat the oven to 350°F and line baking sheets with silicone mats or parchment paper.

In a large mixing bowl, combine cooled brown butter, brown sugar, and granulated sugar; beat with an electric mixer for 3 to 4 minutes until light and creamy.

Add the cooled pumpkin, egg, egg yolk, and vanilla, and beat until combined.

Add the flour, cinnamon, baking soda, salt, allspice, nutmeg, cloves, and cardamom; beat until no streaks of dry flour remain. Fold in the chopped chocolate.

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

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

Allow the cookies to cool on the baking sheet for 5 minutes before transferring to a cooling rack.