Preheat your oven to 350°F.
In a large bowl, cream together the brown sugar and butter until light and fluffy.
Add the molasses and vanilla extract, mixing well until fully combined.
In a separate bowl, whisk together the flour, cinnamon, ginger, cloves, nutmeg, baking soda, and salt.
Gradually mix the dry ingredients into the wet mixture until a stiff dough forms.
Divide the dough in half, wrap each portion in plastic wrap, and chill for 1 hour.
Roll the dough about ⅛ to ¼ inch thick on a lightly floured surface. Cut into shapes using cookie cutters.
Place cookies on a parchment-lined baking sheet and bake for 6–8 minutes, or until edges are crisp.
Let cookies cool for 5 minutes on the baking sheet before transferring to a wire rack.
In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until smooth.
While cookies are still slightly warm, brush the glaze over the tops using a pastry brush.
Let cookies cool completely on a wire rack until the glaze is set.