Combine molasses, brown sugar, and shortening in a large bowl; beat with an electric mixer until smooth and creamy. Add cold water and blend until smooth. (Shortening may separate a bit; this is fine.)

Sift together flour, baking soda, cinnamon, cloves, allspice, ginger, and salt in a separate bowl. Add flour mixture to molasses mixture, blending until incorporated and dough is soft. Shape dough into 2 balls and place in the refrigerator until chilled, 10 to 15 minutes.

Preheat the oven to 350 degrees F (175 degrees C). Spray a baking sheet with cooking spray.

Working in batches, place one ball of chilled dough on a lightly floured surface and roll to 1/4-inch thickness, or 1/2-inch thickness for softer cookies. Cut out cookies with desired cookie cutters and place 1 inch apart on the prepared baking sheet. Repeat with remaining dough.

Bake cookies in the preheated oven until edges are firm, 12 to 13 minutes. Transfer to a wire rack immediately after baking to cool. Allow to cool completely if frosting.