Whisk molasses, water and egg in a small bowl; set aside.
If using an electric mixer: Mix flour, sugar, baking soda, salt, orange peel, ginger, cinnamon, cloves, nutmeg and allspice in large mixing bowl. Cut in butter using a pastry blender or 2 knives until the mixture resembles coarse meal. Pour molasses mixture over flour; beat with mixer until dough forms.
If using a food processor: Place flour, sugar, baking soda, salt, orange peel, cinnamon, ginger, cloves, nutmeg and allspice in food processor; process 10 seconds. Add butter; process until dough resembles coarse meal, about 30 seconds. Pour molasses mixture over flour and process until dough forms. Remove dough from processor.
Turn out on lightly floured surface. Knead 2 to 3 minutes. Transfer dough to bowl; cover. Chill a minimum of 2 hours.
Preheat oven to 350º F.
Roll dough between 2 sheets of waxed paper to 1/8-inch thickness. Cut with cookie cutters. Place on baking sheets; bake for 10 to 12 minutes. Cool.
Melt shortening and white baking chocolate in heavy saucepan over medium heat. Dip half of each cookie in chocolate. Place on cooling racks or wax paper to let chocolate harden.