Preheat oven to 375°F. Grease a 10x15-inch sheet pan; set aside.
In a large bowl, whisk together flour, cinnamon, ginger, allspice, baking soda and salt. Set aside.
In a large mixing bowl, cream sugar and butter using an electric mixer. Scrape down sides of bowl as needed. Add molasses and egg. Mix, scraping down sides with each addition.
Add dry ingredients to the sugar mixture, mix on low speed. Spread dough onto prepared sheet pan. Bake 8 to 10 minutes, until center is cooked. Cake tester poked into the middle should come out clean, and cookie should have an internal temperature of 165°F. Set aside to cool.
Break the pan cookie into several pieces and add to a food processor. Pulse until it becomes fine crumbs. Add water, oil and vanilla. Process on high until all of the ingredients are blended together and creamy. It may be necessary to scrape the bowl once or twice during the processing.
Spoon cookie butter into jars with tight-fitting lids. Tap the jars lightly onto a towel-covered surface to remove any air bubbles.
Store the jars in the refrigerator for up to 1 week.