Preheat oven to 350F. Line a muffin tin with baking cups and spray with cooking oil. Set aside.
Combine the flax meal with the hot water and let stand to thicken for at least 10 minutes.
Add the vinegar to the soy milk to sour then add the vanilla extract.
In a large bowl, sift the flour with the baking powder and salt.
In a separate medium bowl, cream the vegan butter with the sugar until light and fluffy (this may take about 2-3 minutes on medium to high speed).
Add the flax paste to the butter mixture while mixing on medium speed, scrape the bottom and sides of the bowl to incorporate evenly, whip on high for 30 seconds.
Add about 1/2 of the flour to the creamed mixture while mixing on low speed just until combined, then add half of the remaining soured milk.
Add the other 1/2 of the flour and then the remaining sour milk.
Portion the batter between your greased and parchment lined muffin tins and bake immediately approximately 19-25 minutes or until they are springy to the touch when you gently press the centers.
Meanwhile prepare the buttercream recipe by combining everything together with a hand mixer. Pipe icing onto cupcakes and enjoy!