In a medium bowl, whisk together all of the dry ingredients: all-purpose flour, cinnamon, cream of tartar, baking soda, and salt.
In a stand mixer using the paddle attachment (can alternatively use hand mixer or whisk), cream the butter and sugar on medium speed until smooth, about 1-2 minutes. Scrape bottom of bowl.
Add vanilla and pink food coloring and mix until smooth. Add more pink food coloring until you get the shade of pink you desire.
Dump in all of the dry ingredients and mix until combined. If the dough is crumbly, slowly add 2-4 tbsp of dairy-free milk until it comes together. The finished dough should be thick.
Preheat oven to 375°F/190°C and line two baking trays with parchment paper or silicone mats.
In a small bowl, combine granulated sugar and cinnamon for rolling the dough.
Use small cookie dough scoop to gather dough (about 1 ½ tablespoon each). Roll dough into cinnamon sugar mixture, shape into ball, then place onto lined baking tray. This will be the pig's head.For the ears, take ½ tsp of dough, roll into cinnamon sugar mixture, and shape into a triangle using your fingers. Place the ear on the upper left or right side of the head and repeat for the other ear.Place pigs about 3-4 inches apart. They will not spread much while baking.
Bake for 8-10 minutes. Cookies should look puffy, soft, and retain their pink color. They should not be browned.
Let cool on pan for about 5 minutes, then transfer to wire rack. Let cool completely.
To add the faces, use pink and black colored vegan royal icing (recipe in notes below). Place into small piping bags and cut a small tip. First, use the pink to add the noses and ears, then black color for the eyes and nostrils.