In a small pot over medium heat, melt butter, stirring frequently. After a few minutes, the butter will start to turn amber and smell nutty.
Pour brown butter into the bowl of your stand mixer and allow to cool to room temperature.
Once the brown butter is room temp, attach paddle to mixer. Beat butter and sugar on medium-high until light and fluffy.
Beat in cardamom and egg.
In a medium bowl, whisk together flour, baker’s ammonia, and salt. Add half of the flour mixture to butter mixture, mixing on low until it’s almost all incorporated. Scrape down bowl and beater. Repeat once more with rest of flour mixture, increasing speed to medium to create a smooth dough.
Form dough into two logs about 7 inches long. (Each log will be about 250g.) Wrap tightly in cling film and refrigerate for at least two hours or overnight.
When your dough has chilled and you’re hankerin’ for some cookies, heat oven to 350°F. Line baking sheet with parchment paper.
Retrieve one dough log from fridge. Using a sharp knife, slice dough into 20 coins about ⅓" thick.
Place cookies on prepared baking sheet. Lightly brush each cookie with milk.
Bake for 18–20 minutes, turning sheet after 10 minutes. Cookies are done with they’re golden brown and set.
Transfer cookies to a wire rack to cool completely.
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