Preheat the oven to 350°F. Line muffin tins with cupcake liners and set aside.
Cream together the butter and sugar in the bowl of a stand mixer, or you can also use a hand mixer. Beat for 2 minutes on medium speed, scraping down the sides of the bowl midway. The mixture will be fluffy and very pale yellow.
Beat in lemon zest, vanilla extract, lemon oil, and eggs. Beat for 2 minutes longer.
Measure the flour, baking soda, and baking powder into a separate bowl and whisk together.
In another small bowl, whisk together milk, mayonnaise, and lemon juice.
Add ⅓ of the milk mixture to the butter/sugar mixture and beat until combined. Add ½ of the flour mixture, mixing briefly. Add another ⅓ of the milk mixture, the remaining flour, and then the remaining milk mixture.
Beat just enough between each addition to incorporate the ingredients, but do not overmix.
Transfer batter to the prepared muffin tins, filling ⅔ of the way full.
Bake for 17 minutes or until a toothpick inserted into the cupcakes comes out with just a few crumbs.
After 3 minutes of cooling, transfer cupcakes to a cooling rack to cool completely.
Use a serrated spoon or piping tip to scoop out a small portion (about 1 teaspoon) of the top of each cooled cupcake.
Use a piping bag, a Ziploc bag with the corner snipped off, or a squeeze bottle to fill each cavity with lemon curd.
Prepare the strawberry frosting.
Frost the cupcakes to cover the lemon curd.
Do not overmix the batter once you have added all of the ingredients together. This can make tough cupcakes.
Oven temperatures vary and may need to be recalibrated periodically to ensure they are accurate. Make sure to keep a close eye on your cupcakes as the recommended baking time approaches.
This is a medium-density, moist cupcake. The cupcakes hold up well to frosting once cooled, but it is too soft while it is still warm. Wait until the cupcakes are cooled completely (you can even chill them in the refrigerator or freezer) before scooping the tops and filling them with lemon curd or adding frosting.