In a medium saucepan, melt the butter over low heat. Continue cooking, stirring frequently, until the butter foams and turns a rich amber color with brown specks at the bottom, emitting a nutty aroma. Remove from heat immediately.

Once butter is browned, remove the saucepan from heat and transfer the butter to a mixer bowl to cool to become thicker again.

In a large mixing bowl, combine the cooled browned butter, brown sugar, and granulated white sugar. Using an electric mixer on medium speed, cream together for approximately 2 minutes until the mixture is well combined.

Measure out the pumpkin purée, then place it on a plate lined with paper towels. Use another paper towel to blot the pumpkin to remove as much liquid as possible.

Add the egg yolk, vanilla, sourdough discard, and reduced pumpkin puree to the sugar butter mixture. Mix all of the wet ingredients on LOW until just combined.

In a separate bowl, whisk together the flour, cream of tartar, baking soda, cinnamon, ginger, nutmeg, cardamom, and salt.

Mix the dry ingredients into the wet ingredients on low just until no dry streaks remain.

Using a 2-ounce cookie scoop, portion out your cookie dough and roll into balls. Transfer to a parchment lined baking sheet, and cover with plastic wrap. Transfer to the refrigerator to chill for at least 2 hours.

Preheat the oven to 350°F. Allow the cookies to rest at room temperature while your oven preheats.

Stir together the granulated sugar, cinnamon, ginger, nutmeg, and cardamom in a small bowl.

Roll the cookie dough balls well in the cinnamon sugar mixture.

Arrange the cookies on a parchment-lined baking sheet with plenty of room between them for spreading.

Smash down the tops of the dough balls slightly with your palms, and sprinkle the tops with more cinnamon sugar mixture.

Bake the cookies for 16–18 minutes, or until the edges are set and the centers still look slightly soft.

Let the cookies cool on the baking sheet for about 5 minutes before transferring them to a wire rack.