Cream the 1/2 cup vegan butter in the bowl of a stand mixer fitted with the paddle attachment for 1-2 minutes or until it is light and fluffy. Scrape down the sides of the bowl with a silicone spatula.
Pour the 2 1/2 cups powdered sugar and 1/2 cup cocoa powder in a medium sieve and sift in 1/2 cup batches (just estimate, it doesn't need to be exact) over the butter. Add a splash of the plant-based milk and beat on low until incorporated. Continue adding in batches and beating on low until all ingredients have been incorporated.
Add the 1 1/2 teaspoons vanilla and 1/4 teaspoon salt and beat on medium until light and fluffy, about 3 minutes. Stop as soon as you have smooth, creamy, fluffy frosting. Don't overmix or you will create big air bubbles.