Preheat oven to 350F and prepare 18 cupcake liners in a muffin pan. In a small bowl, whisk together the ground flaxseed with the water and set aside to thicken.
In the bowl of a stand mixer, combine the flour, baking powder, baking soda, salt, sugars, cinnamon, ginger, nutmeg, and cloves.
Add in the vegan butter, and beat on low until it's incorporated and has a sandy texture.
In a small bowl, whisk together the oil, flaxseed mixture, nondairy yogurt, fresh grated ginger, molasses, and vanilla extract, and add them to the dry ingredients. Mix until combined.
Finally, pour in the unsweetened nondairy milk, and beat on medium-low until smooth and creamy.
Divide batter evenly among the prepared cupcake liners, and bake for 20-25 minutes until cake is set in the center and a toothpick comes out clean.
While the cupcakes cool, prepare the frosting.
In the bowl of a stand mixer, beat the shortening, vegan butter, vanilla, and eggnog super-strength flavoring together until completely smooth and creamy. Add in the powdered sugar, 1 cup at a time, until a thick frosting forms. Add some vegan eggnog as needed to make frosting lighter and fluffier. Add more eggnog flavoring to taste.
To decorate, transfer frosting into a piping bag fitted with a large star tip. Pipe frosting on top of gingerbread cupcakes, and decorate with the Sweets & Treats sprinkles. Enjoy!