To a food processor, add your rinsed and patted dry fresh basil, as well as your granulated sugar. Pulse until ingredients are mixed and then add cornstarch, pulse until you have the texture of powdered sugar. Now you have basil-flavored powdered sugar!
In the bowl of a stand mixer fitted with the paddle attachment, or in a large mixing bowl using a handheld mixer, beat the unsalted butter, basil-infused powdered sugar, salt, heavy cream or milk, and vanilla extract on low for about 30 seconds before increasing speed to medium high for 5 minutes.
Test taste and add a drop or two of lemon juice to cut sweetness if desired.
Set aside frosting in bowl until ready to use for topping cupcakes. You’ll then add it to a piping bag fitted with a tip of your choice or use a spoon or spatula to spread it onto your baked goods.
