Preheat the oven to 350°F, and line a muffin pan with cupcake liners.
Mix together the flour, cocoa powder, sugar, baking power, and salt in a large bowl. Then add in the non-dairy milk, neutral oil, applesauce (if using it), and vanilla extract and mix until just combined. I like to add all the batter into a large measuring cup to help pour it evenly into the cupcake tin.
Fill each cupcake liner evenly with the batter. They should fill around 3/4 of the way up.
Bake at 350°F for 20-24 minutes. I find my sweet spot is 22/22.5 minutes. You want a toothpick inserted into the cupcake to come out with crumbs, but no wet batter.
Remove the pan from the oven and let cool for 10-15 minutes in the pan before moving cupcakes to a cooling rack.
While cooling, make the frosting by mixing the cold vegan butter, powdered sugar, cocoa powder and salt using a mixer of some sort. You will want to add the non-dairy milk towards the end depending on how your consistency comes out. I find 1-2 tbsp to work perfectly, but if your frosting is still too stiff, add some more milk. If it's too loose, add more powdered sugar.
When the cupcakes are fully cooled, generously frost them.
Eat and enjoy!