Ingredients

1 1/2 cups unbleached all-purpose flour, plus more for dusting 

3 tablespoons Dutch-process cocoa powder 

3/4 teaspoon kosher salt 

1 teaspoon ground ginger 

1/2 teaspoon ground cinnamon 

1/4 teaspoon ground cloves 

1 stick unsalted butter, room temperature 

3/4 cup packed light-brown sugar 

1 tablespoon grated fresh ginger (from a 2-inch piece) 

1/2 teaspoon baking soda 

1 large egg, room temperature 

2/3 cup confectioners' sugar 

2 tablespoons Cointreau or strained orange juice, plus more if needed 

1 tablespoon melted unsalted butter 

Pinch of kosher salt 

Preparation

Cookies: Preheat oven to 375°F. Whisk together flour, cocoa, salt, ground ginger, cinnamon, and cloves. In a large bowl, beat butter with brown sugar, fresh ginger, and baking soda until creamy. Add egg; beat to combine. Reduce speed to low; beat in flour mixture.

Scoop a scant 1/4 cup of dough (1.75 ounces); roll into a ball. Dust a cookie stamp with flour, tapping out excess. Place dough in center of stamp, then press evenly to cover shape of design. Place, dough-side down, on a parchment-lined baking sheet and press until dough is about 1/4 inch thick.

Carefully remove (if it sticks, just gather up dough and start over). Repeat with remaining dough, arranging cookies 2 inches apart. Refrigerate 20 minutes; use a 2 3/4-inch round cutter to trim excess. Bake until firm to the touch, 11 to 13 minutes.

Glaze: Meanwhile, whisk together confectioners’ sugar, Cointreau, butter, and salt; glaze should have the consistency of honey. (If too thick, whisk in more Cointreau.) Let cookies cool on sheets on a wire rack 8 minutes, then brush with glaze. Let cool completely. Cookies can be stored in an airtight container at room temperature up to 3 days.

Omit cocoa powder. Increase flour to 1 2/3 cups, increase brown sugar to 1 cup, and increase butter to 1 1/2 sticks. Beat in 6 ounces (1 1/2 cups) chopped semisweet chocolate at end of step 1. Use a 1 1/2-inch scoop to make balls (about 2 tablespoons). Roll in sanding sugar, then place about 2 inches apart on parchment-lined baking sheets. Refrigerate 20 minutes. Bake, rotating sheets once, until cookies are just set but still a little bit soft in center and slightly darker around edges, 12 to 13 minutes. Omit glaze.