In a measuring cup, combine the soy milk and apple cider vinegar. Let sit a few minutes until it curdles (this is your vegan buttermilk).
In a large mixing bowl, beat the softened vegan butter and sugar with a hand mixer (or stand mixer) until light and fluffy, about 1-2 minutes. Add the lemon zest, lemon extract and vanilla and beat to combine.
With the mixer on low speed, add in the soy milk/vinegar mixture and mix for 30 seconds.
Now add the flour, then sprinkle the baking powder and salt on top of the flour. Mix on low speed until well combined, scraping the sides as needed with a spatula.
Fill the liners 3/4 full and bake for 20-24 minutes, until a toothpick inserted comes out clean and they are lightly golden on top. Let them cool completely before frosting.
For the Lemon Buttercream Frosting:
Wipe out the bowl you used for the cupcakes and rinse the beaters from your mixer. Beat the vegan butter until light and fluffy, about 2 minutes. Add in 2 cups of the powdered sugar, lemon juice, lemon zest and vanilla. Beat on low, then switch to medium speed and beat until light and fluffy, about 2 minutes.
Now add in the remaining 2 cups of powered sugar and mix. If the frosting seems too thick, add a tablespoon at a time of soy milk. If the frosting gets too thin, add a little more powdered sugar until a spreadable, thick frosting consistency is reached.
Pipe frosting onto cooled cupcakes or simply spread it on with a butter knife.
May substitute almond, coconut or hemp milk for the soy if desired. I think soy milk makes the best vegan buttermilk though.
For the cupcakes, softened coconut oil could be substituted for the vegan butter, but it won't work in the frosting. You really need vegan butter for the buttercream frosting.