Preheat oven to 350° and line two muffin tins with 18 cupcake liners. In a large bowl using a hand mixer, beat butter and sugar until light and fluffy. Add eggs, one at a time, beating well after each addition. Add lime juice and zest and vanilla and mix until combined.
In another large bowl, whisk together flour, cornstarch, baking powder, and salt. Add half the dry ingredients to the wet ingredients, beating until just combined. Pour in milk and mix until fully incorporated. Add remaining dry ingredients and stir until just combined. Fill cupcake liners ¾ full with batter.
Bake until slightly golden and a toothpick inserted into center of each cupcake comes out clean, about 25 minutes. Let cupcakes cool in pans 5 to 10 minutes, then transfer to a wire rack to cool completely.
