01 - In a medium bowl, whisk together the flour, ginger, cinnamon, nutmeg, cloves, baking soda, and salt until well combined.
02 - Using a mixer, beat the softened butter, brown sugar, and granulated sugar on medium speed for 2–3 minutes until light and fluffy.
03 - Add the molasses, egg, and vanilla extract to the butter mixture and blend thoroughly.
04 - Gradually add the dry ingredient mixture to the wet mixture and mix just until a soft dough develops.
05 - Divide the dough into two equal portions. Roll each portion between two sheets of parchment paper into a 9 by 7-inch rectangle approximately 1/4 inch thick.
06 - For the filling, combine melted butter, brown sugar, and ground cinnamon in a small bowl. Mix until uniform.
07 - Spread half the cinnamon filling evenly over each dough rectangle. Starting from one long edge, roll each rectangle tightly into a log, wrap with parchment, and refrigerate for at least 45 minutes until firm.
08 - Set oven to 350°F. Line baking sheets with parchment paper.
09 - Cut each chilled log into 1/2-inch rounds using a sharp knife. Space the cookies 2 inches apart on the prepared baking sheets.
10 - Bake for 10–12 minutes until the edges are set and cookies are lightly golden. Allow cookies to cool on the pan for 5 minutes, then transfer to a wire rack.
11 - Whisk the powdered sugar, milk, and vanilla extract until smooth. Drizzle the glaze over cooled cookies.