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 in ½ of the flour mixture, mixing briefly. Add in 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 the 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.