01 - In a medium mixing bowl, whisk together flour, ginger, cinnamon, nutmeg, cloves, baking soda, and salt until evenly blended.
02 - In a large bowl, beat softened butter, brown sugar, and granulated sugar until pale and fluffy, approximately 2 to 3 minutes.
03 - Add molasses, egg, and vanilla extract to the butter mixture. Beat until fully integrated and smooth.
04 - Gradually add dry ingredients to the wet mixture, mixing until a uniform, soft dough forms.
05 - Divide dough evenly. Roll each portion between two sheets of parchment paper into a rectangle measuring 9 by 7 inches and 1/4 inch thick.
06 - Mix melted butter, brown sugar, and cinnamon for the filling. Evenly spread half the mixture over each rectangle of dough.
07 - Starting from the long edge, gently roll the dough rectangles into tight logs. Wrap each log in parchment paper and refrigerate for at least 45 minutes until firm.
08 - Preheat oven to 350°F (175°C). Line baking sheets with parchment paper.
09 - Cut each chilled log into 1/2-inch thick rounds. Arrange on prepared baking sheets, spacing 2 inches apart.
10 - Bake cookies for 10 to 12 minutes, or until edges are set and lightly golden. Let rest on baking sheets for 5 minutes, then transfer to wire racks to cool completely.
11 - Combine powdered sugar, milk, and vanilla for the glaze. Whisk until smooth. Drizzle over cooled cookies.