Preheat the oven to 350 degrees. Prepare baking sheets by lining with parchment paper or lightly spraying with non-stick cooking spray.
In a mixing bowl, cream the shortening and sugar. Add the molasses, vinegar, and vanilla. Mix well.
Add the baking soda, cinnamon, salt, and cloves. Mix well.
Stir in 3 cups of the flour. Add the water; mix well. Add the 2 remaining cups of flour.
Turn the cookie dough out onto a lightly floured surface. Roll the dough out to ¼ inch thick. You can sprinkle the dough with a little flour if it is sticking to your rolling pin.
Cut out the gingerbread men and place them on prepared baking sheets.
Bake at 350 degrees for 12 minutes.
Make icing by whisking the vanilla and milk a little at a time into the powdered sugar until desired consistency is reached. It should have a consistency a little thicker than syrup.
Ice the gingerbread men a while they are still just slightly warm. Leave them on your countertop until the icing is set. This will take an hour to two hours. Test by lightly touching the icing top. It should not be soft or squishy.
Store the cookies in an airtight container with wax paper in between the layers. Allow the cookies to sit overnight for best flavor and maximum softness.