Preheat the oven to 350 degrees.
Add the ½ cup salted butter to a saucepan and melt on medium-low heat. Once melted, increase the heat to medium and stir constantly until it turns a golden brown color. Remove from the heat and pour the butter into a heat-safe bowl. Cool at room temperature for 5 minutes.
½ cup salted butter
Stir in the 1 tbsp fresh ginger, 1 tsp cinnamon, ½ tbsp ground ginger, 1 tbsp espresso powder, and ½ tsp nutmeg. Cover and chill the butter mixture in the fridge for 30 minutes.
1 tbsp fresh ginger, ½ tbsp ground ginger, 1 tbsp espresso powder, ½ tsp nutmeg, 1 tsp cinnamon
In a bowl, whisk together the 1 cup flour, 1 tsp salt, and ½ tsp baking soda and set aside.
1 cup flour, 1 tsp salt, ½ tsp baking soda
Once chilled, add the butter mixture to the bowl of an electric mixer fitted with a paddle attachment and beat on medium-high speed until light and fluffy, about 3 minutes. Add the 1 cup brown sugar and beat to combine. Add the 1 egg yolk and 1 tbsp molasses and mix until incorporated and smooth.
1 cup brown sugar, 1 tbsp molasses, 1 egg yolk
Use a spatula to fold in the dry ingredients until a dough forms. Form 2-3 tbsp sized balls out of the dough and coat each in the ¼ cup granulated sugar. Place the dough balls on a baking sheet lined with parchment paper at least two inches apart. Use a glass to press the dough down to about 1 inch thickness.
¼ cup granulated sugar
Bake for 10-12 minutes. Remove from the oven and let cool for at least 30 minutes at room temperature.
In a small bowl, whisk together the 1 cup powdered sugar, ½ tsp cinnamon, and ½ tsp espresso powder. Add the 3 tbsp whole milk and whisk until a smooth icing forms.
1 cup powdered sugar, ½ tsp espresso powder, ½ tsp cinnamon, 3 tbsp whole milk
Dip half of the cooled cookies into the icing and place on a plate or baking sheet lined with parchment paper. Chill for at least 30 minutes until the icing is set.