Prep the Oven: Start by preheating your oven to 350°F (180°C) and position the rack in the center. Line a standard cupcake pan with paper liners and set it aside.
Combine the ingredients: In a medium bowl, whisk together the oil and sugar until well combined. Add the eggs and beat with an electric mixer on medium speed for about a minute, until the mixture looks light and smooth. Next, add the gluten-free flour, salt, baking powder, dairy-free milk, and vanilla extract (or vanilla paste). Mix again on medium speed for another minute, until everything is blended into a smooth batter.
Fill the Liners and bake: Scoop the batter evenly into your cupcake liners, filling each about two-thirds full. Bake for 18 to 20 minutes, or until the tops are lightly golden and spring back when gently touched. Let the cupcakes cool in the pan for about five minutes, then transfer them to a wire rack to cool completely before adding any frosting.
Making the Dairy-Free Frosting: In a clean bowl, beat the dairy-free butter and vanilla paste together until smooth and fluffy. Slowly add the powdered sugar, one cup at a time, beating well between each addition. Alternate with a tablespoon of dairy-free milk as needed to keep the frosting smooth and spreadable.
Serve: If the frosting feels too thick, add a splash more milk until you reach your desired consistency. Once your cupcakes are fully cooled, frost generously and enjoy!