Make the Flax Egg: In a small bowl, stir the flaxseeds and water together, then set aside to thicken.
In a medium-large bowl, whisk together the flour, cinnamon, ginger, nutmeg, cloves, baking soda and salt. Set aside.
In a large bowl with a hand mixer (or stand mixer using the paddle attachment), beat the vegan butter and brown sugar together for 2-3 minutes until creamy and fluffy.
To the bowl with the butter/brown sugar mixture, add the flax egg, molasses and vanilla. Beat on medium speed until smooth and well combined.
Gradually add the flour mixture on low speed until just combined.
Divide the cookie dough into two portions. Form each portion into a ball, then flatten with your hands into about a 1 inch disk (I used parchment paper on a counter to flatten). Wrap the discs in plastic wrap and chill in the refrigerator for at least 1 hour. Overnight is fine as well if you want to prepare the dough a day ahead of time. If the dough was chilled longer than an hour, let it sit at room temperature for 20 minutes before rolling.
Once the dough has chilled, preheat the oven to 350 degrees F and line a large baking sheet (or 2) with parchment paper.
Sprinkle flour on a clean, large surface (I just use my counter). Unwrap the dough and place on the floured surface. Using a rolling pin, roll the dough until about 1/8th inch thick. Use cookie cutters to cut them into shapes, and transfer to the baking sheet.
Bake for 8-10 minutes (for crispy cookies, bake for 12-14 minutes), in the center rack of the oven. They will be quite soft out of the oven, so let them cool on the pan for 5 minutes before transferring to a wire rack to finish cooling.
Repeat rolling and cutting until all the dough is used.
Make the simple icing: Whisk all icing ingredients together in a medium bowl until very smooth. You want it to be fairly thick for decorating, so add more powdered sugar as needed, or more milk if it gets too thick.
Once the cookies have cooled completely, use a piping bag or plastic bottle to decorate the cookies however you like. Enjoy! Store leftover cookies in a covered container for 4 days, or freeze them.