Preheat the oven to 350 F. Place paper liners in a 12-cup muffin pan.
In a small bowl, whisk together the flour, baking powder, and salt.
In the bowl of an electric stand mixer, beat the butter until creamy. Add the sugar and beat for 3 to 4 minutes, or until light and fluffy. Add the egg and egg white, beating on medium speed until combined. Add the oil, lemon zest, vanilla, and lemon extract and beat for 1 to 2 minutes, or until combined. With the mixer on low speed, add half of the dry ingredients. Pour in the milk with the mixer on and mix to combine. Pour in the rest of the dry ingredients and mix on medium speed until the batter is combined.
Fill the cupcake liners three-quarters of the way full. Place the pan on a baking sheet and bake for 16 to 18 minutes or until golden on top and set in the center. Let cool completely before frosting.
In the bowl of an electric stand mixer fitted with the paddle attachment, combine the butter and cream cheese and beat until creamy. With the mixer on low speed, gradually add the powdered sugar. Increase the speed of the mixer and beat the frosting, scraping down the sides of the bowl as needed, until fluffy and combined. Beat in the vanilla, lime zest, and rum.
Frost the cupcakes and garnish with the fresh mint.