Gather and measure all ingredients before you start.
Whisk flour, baking soda, salt, ginger, cinnamon, allspice and cloves in a medium bowl.
Beat butter and brown sugar until smooth, about 1 minute. Beat in molasses, then egg and vanilla; scrape bowl once.
Add dry ingredients, mix on low until a soft dough forms, no dry flour remains. Dough will be sticky — that is correct.
Divide in half, shape flat discs, wrap, chill at least 3 hours or overnight. Do not skip.
Heat oven to 350°F (175°C). Line sheets with parchment.
Roll one disc to even 1/4 inch (6 mm) on lightly floured surface. Cut shapes, place 1 inch apart, chill cut shapes on sheet 10 minutes.
Bake 9-11 minutes: edges set, surface matte, centres still slightly soft.
Cool on sheet 5 minutes, move to rack, cool completely before icing.
Icing: whisk powdered sugar, milk, vanilla, salt to thick pipe-able consistency; pipe outlines, let set about 30 minutes before stacking.