In a large bowl, whisk together the flour, ginger, cinnamon, allspice, baking soda, and salt. Set aside.

Put the brown sugar and shortening in the bowl of an electric mixer fitted with the paddle attachment. Beat at high speed until light and fluffy, then add the molasses, eggs, and vinegar and beat until combined. Add the flour a little at a time, mixing on low speed between additions and scraping down the bowl as needed, and then beat on low until all the flour has been incorporated and the dough clumps together. Cover and refrigerate the dough for at least 1 hour.

Preheat the oven to 350°F. Line two large baking sheets with parchment.

Divide the dough into four pieces and shape each into a disk. Place one disk on a lightly floured counter; keep the remaining three covered in the refrigerator while you cut the cookies. Roll out the dough to an approximate ⅛-inch thickness. Cut out your shapes, using the bear cookie cutter and the rim of a pint glass for the pizzas (or whatever shapes you like!), and transfer them to one of the prepared cookie sheets. (Once you've cut the shapes, roll out the dough one more time and cut some more.) For each bear, scoop ¼ of dough and roll it into a ball with your fingertips. Press the ball into the faces to make snouts. Press a piece of raisin into each snout for a nose, and press two pieces of raisin on top of the snout for eyes. For the pizzas, rip off pieces of dough scraps and press them into the edges to make the crust.

Repeat with the remaining dough, and bake the cookies for 8 to 10 minutes, until just set. Remove the cookies from the oven and transfer to wire racks to cool completely.

Wash and dry your mixer bowl and paddle attachment. Place the confectioners' sugar and egg white in the bowl. Beat on low speed until combined, then stream in the water. Increase the speed to medium and beat until the mixture holds stiff peaks when you lift the paddle (about 8 minutes). If the icing is too stiff, add a little more water; if it's too thin, add a bit more sugar.

Divide the icing between two small bowls.

Use your food coloring to tint one bowl of icing a nice deep red, stirring well to make sure the color is consistent throughout. Scrape half of the red icing into a small plastic zip-top bag. Keep all the icing covered with plastic until the cookies have cooled completely and you're ready to decorate them.

For the bears: Snip a tiny bit off one of the bottom corners of the bag of red icing and twist the top to make a little piping bag. Carefully pipe a heart on the top right side of each bear's body.

For the pizzas: Spoon some red icing onto each pizza and spread it out all the way to the crust, making it a little messy so it looks like marinara sauce. Let it harden (30 minutes or so). Spoon some white icing on top of the red icing to make "cheese," spreading it in all directions and making sure not to cover the red "sauce" completely. Immediately top the white icing with chopped raisins (olives/sausage) and sprinkles or sugar (basil/arugula/peppers).

Let the icing harden completely before stacking. Enjoy!