In a medium bowl, whisk together flour, cinnamon, ginger, nutmeg, cloves, salt and baking soda. In a large bowl using either a hand or stand mixer, beat softened butter with both granulated and brown sugar and molasses until creamy.
Add in egg and vanilla extract, beating until smooth. Add in the dry ingredients in three separate additions, beating after each until fully incorporated. Divide the dough in half and wrap each half in plastic wrap. Refrigerate for at least 4 hours or overnight.
Preheat oven to 350 F. Roll out cookie dough and cut out cookies with a gingerbread cookie cutter. Place cookies onto a ungreased baking sheet and bake for 10-12 minutes. Let cool completely.
For the icing, in a small bowl, combine the powdered sugar with corn syrup, milk and vanilla extract. Place the icing into a piping bag and pipe icing onto cooled down cookies.