In a mixing bowl, sift the flour, baking soda, spices, and sea salt together and whisk to combine. Set this aside.
In the bowl of a stand mixer, or another large mixing bowl if you're using a hand mixer, cream the vegan butter and brown sugar together for about 2 minutes until smooth, well combined, and fluffy.
Add the molasses, nondairy milk, and vanilla extract and continue beating until well combined.
Add the flour mixture in portions while continuing to mix on low. It will come together into a smooth, well combined, but not too sticky dough. Dump the dough onto a large piece of plastic wrap. If your dough seems a bit soft to handle, just portion it out with a spoon or spatula from the bowl onto plastic wrap and fold over the edges to form a ball of dough in the plastic wrap. Refrigerate for at least 1 hour to firm up. The dough can last refrigerated for about 3 to 4 days. If you've refrigerated it longer allow it to sit on the counter for 15 to 20 minutes before rolling out.
When you're ready to roll out the cookies, preheat the oven to 350°F.
To roll out the cookies, flour a clean surface and a rolling pin. Portion the ball of dough in half and work with one half at a time. Keep the other piece wrapped in plastic in the fridge. Roll out the dough until it's approximately 1/8 to just under 1/4-inch thick. Lightly flour the base of your cookie cutter and cut shapes.
Gather the excess, which you can roll out again. Lift the cut-out cookies from the counter with a lightly floured spatula/lifter and place them on parchment lined baking sheets. Continue to flour your rolling surface and rolling pin, roll out the excess dough, and cut out more cookies until there is no dough left.
Bake 2 baking sheets at a time on the middle 2 racks of the oven for about 9 to 11 minutes. You will notice the cookies rise a bit or poof and then fall. About a minute after they fall is when they're about done. Do not let the edges or bottoms get too browned. Remove the baking sheets onto wire racks for about 5 to 10 minutes. Then lift the cookies off and place on the wire racks to cool completely before icing.
To make the piping icing, combine confectioners' sugar and water together in a mixing bowl with a whisk. It should be a stiff but still sort of a fluid consistency. It shouldn't drip or spread on the cookies, but rather hold its shape in a thin line or dot. Transfer the piping icing into a piping bag or a squeeze bottle with a fine tip at the end and decorate your cookies as desired. If you want to use blue icing as well, take about a third of this icing and add 1 to 2 drops of blue food coloring and combine well.
You can pipe icing as the outline to your cookies and then "flood" the cookies with flood icing. For the flood icing, combine confectioners' sugar and water together in another mixing bowl using a whisk. This will be a runnier icing that will flood the surface of your cookies that have been outlined. Use a small offset spatula or knife to spread the flood icing around the surface of the cookies between the outlines.
After flooding the cookies with this icing, allow it dry about half way through or dry to the touch, so that when you go to pipe more icing in the opposite color on top it doesn't totally melt into the flood icing.
Allow the icing to dry and harden completely before placing in cookie tins or containers.
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