1Preheat oven to 350 degrees F (175 degrees C). Grease or line 12 muffin cups with paper liners.
2Beat white sugar, 1/2 cup butter, eggs, and 2 teaspoons lemon extract together in a bowl using an electric mixer until smooth and creamy; add baking powder and salt and beat until smooth. Slowly mix flour, alternating with cold milk, into butter mixture until batter is just mixed. Spoon batter into the prepared muffin cups.
3Bake in the preheated oven until a toothpick inserted in the center of a cupcake comes out clean, 15 to 20 minutes.
4Beat 3 tablespoons butter, 2 teaspoons lemon extract, and milk together until smooth. Beat confectioners' sugar into butter mixture until desired consistency is reached; spread onto cupcakes.
Footnotes
Cook's Note:
You can easily substitute any extract you like to both the batter and the frosting.
Add food coloring to the frosting if you want it too look "lemony."