Add the vegetable oil, milk, eggs, and vanilla. Whisk to combine-- just until no large lumps of flour remain.
½ cup vegetable oil, ½ cup milk, 2 large eggs, 1 teaspoon pure vanilla extract
Fill each cupcake tin ¾ of the way full and bake the cupcakes until a toothpick inserted into the center comes out clean, about 14-16 minutes.
Allow the cupcakes to cool completely on a wire rack before icing.
For the Frosting
Using a stand or hand mixer, beat the butter, lemon zest, and vanilla extract on medium speed until smooth, about 2 minutes.
½ cup unsalted butter, 1 teaspoon lemon zest, 1 teaspoon pure vanilla extract
On low speed, add the powdered sugar a little at a time.
2 cups powdered sugar
After you’ve added all the powdered sugar, turn the mixer to high speed and beat until the icing is light and fluffy, about 2 minutes.
Transfer the icing to a piping bag fitted with your choice of tip and set aside until ready to use.
Assembly
Scoop a small hole out of the center of each cupcake and fill the center with lemon curd (about 1-2 teaspoons). Place the piece of cake you scooped out back on top of the lemon curd.
½ cup lemon curd
Frost the cupcakes as desired (I did a simple swirl with a Wilton 2D tip).
Notes
If you don't have a lemon zester handy, that's okay! You can use a cheese grater (the side with the smaller holes) to zest your lemon.
When scooping the centers out of the cupcakes, use a cupcake corer for the most exact sizing. However, utensils like a regular spoon will work too.
Beat the icing until it's light and fluffy, then stop. You don't want to overbeat it.
Storage: Store lemon curd cupcakes in an airtight container at room temperature for up to 2 days or in the refrigerator for up to 4 days.