Make lemon custard: Add the soy milk, sugar, and cornstarch to a saucepan and whisk well to remove any lumps. Add the lemon juice and zest and whisk again to combine.
Bring the mixture to a simmer and cook on low heat for about 5 minutes whilst whisking. Alternate between using a whisk and rubber spatula to make sure the custard does not stick to the pan. If you're using a gas hob cook on the lowest setting to avoid the direct heat cooking the mixture too fast.The mixture will become thick once the cornstarch is cooked, remove it from the heat and pass the custard through a fine-mesh sieve into a clean bowl. Set aside to cool to room temperature for 30-40 minutes.
Whisk the butter: Add the vegan butter to a large mixing bowl (or stand mixer if using) and whisk with an electric mixer for 3 minutes, until light and fluffy.
Combine: Slowly add the chilled custard mixture to the butter, one tablespoon at a time, whisking to incorporate it each time. Once you have added all of the lemon custard, continue to whisk the buttercream for another 2-3 minutes until light and fluffy.
Serving and storage: Use to frost vegan cakes or cupcakes immediately, or store in an airtight container and refrigerate for up to 5 days. The recipe will generously frost a 3-layer 6" cake, 2-layer 8/9" cake, or 12-18 cupcakes.Before use, allow the buttercream to come to room temperature for an hour, and then pipe or frost as usual.
Notes
Vegan butter: Take this out of the fridge to sit at room temperature for 1-2 hours. Make sure you use vegan block butter, otherwise known as butter sticks. Spreadable butter from a tub or margarine will throw off the recipe due to its higher water content. I use flora plant butter which is nut-free, coconut-free, and gluten-free.
To freeze: Transfer your frosting to an airtight storage container and freeze it for up to 2 months. Defrost it in the fridge overnight, and re-whip if needed before use.