Preheat oven to 350 degrees. Line a standard muffin pan with paper liners or generously grease with allergy friendly oil; set aside.
In a small mixing bowl, combine water and flaxseed. Whisk well and set aside for 5 minutes to allow mixture to thicken. This will serve as your “egg” in the recipe.
In a separate mixing bowl, whisk together flour, baking soda, and salt; set aside.
In a large mixing bowl, beat sugar and shortening until well combined, approximately 2-3 minutes. If using an electric stand mixer, use the whisk attachment.
Add flaxseed mixture and vanilla and continue to beat until light and fluffy, scraping sides of bowl with spatula as needed.
Sift in flour mixture in three batches, alternating with milk and scraping sides of bowl as needed. If using an electric stand mixer, switch to the paddle attachment for this step. Batter should be smooth and slightly thick. Remember it is important not to over mix your batter.
Fill prepared muffin cups about two-thirds full with batter; bake until tops are springy to the touch and cake tester comes out clean from centers of cupcakes, approximately 18-20 minutes.
Allow cupcakes to cool in pans for 5 minutes. Turn out on a wire rack for remainder of cooling. Once cupcakes are completely cooled, frost with Classic "Buttercream" Frosting [recipe on www.bubblegirlbakes.com] and garnish with allergy friendly sprinkles or topping of choice.