Preheat the oven to 350°F. Line baking sheets with parchment.
Mix dry ingredients (2 min): Whisk flour, baking soda, ginger, cinnamon, cloves, espresso, and salt in a medium bowl.
2 1/4 cups all purpose flour, 1 teaspoons baking soda, 2 teaspoons ground ginger, 3/4 teaspoons cinnamon, 1/2 teaspoon ground cloves, 1/2 teaspoon salt, 2-3 Tablespoons espresso powder
Cream the butter and sugar (3 min): In a stand mixer with the paddle attachment, or bowl with a hand mixer, beat the butter and sugar for 2–3 minutes, until light and fluffy.
2/3 cup unsalted butter, room temperature, 1 cups granulated sugar
Add the wet ingredients (2 min): Add the egg and molasses and beat 1–2 minutes, until fluffy.
1 large egg, 1/4 cup molasses
Mix in the dry ingredients (1 minute): Add dry ingredients on low speed until a soft dough forms.
Scoop and bake (11 min): Using a large cookie scoop (or scant ¼-cup), scoop the dough and roll in coarse sugar. Drop them 2-3 inches apart on the baking sheets. Bake 11–13 minutes, until puffed with cracks forming on the tops. Cool on the baking sheet for 5 minute then transfer to a wire rack to cool completely.
Make the glaze (5 min): Brown butter over low heat. Whisk in the brown sugar and milk. Continue to stir while it bubbles, settles, and the brown sugar dissovles. Remove from the heat and whisk in the powdered sugar. Let it cool slightly to thicken.
6 Tablespoons unsalted butter, 1/4 cup light brown sugar, 3 Tablespoons milk, 1 cup powdered sugar
Glaze the cookies: Use a spoon to drizzle the glaze over the cookies. Leave as is or dust with powdered sugar, espresso powder, or sprinkles.