Preheat oven to 350 degrees F (175 degrees C). Line 12 cupcake cups with paper liners. In a bowl, whisk together the flour and baking powder.
In a mixing bowl, beat the white sugar with 1/2 cup butter until thoroughly mixed, then beat in the eggs, one at a time, incorporating each egg before adding the next. Stir in 2 teaspoons of vanilla extract. Stir the flour mixture into the egg mixture, followed by the milk, mixing to make a smooth batter. Fill each lined cupcake cup about 2/3 full of batter, and push a frozen solid chocolate egg into the batter in the center of each cupcake so a tiny bit of the egg sticks out.
Bake cupcakes in the preheated oven until the tops are lightly browned and the cakes spring back when pushed with a finger, 20 to 25 minutes. Allow cupcakes to cool completely.
In a bowl, beat 1/2 cup of butter with confectioners' sugar and 1/2 teaspoon of vanilla extract; add 1 tablespoon of milk, a teaspoon at a time, until the frosting is smooth. Beat in your choice of food color to desired shade, and spread frosting on each cupcake. Top each cupcake with a candy-coated mini egg for decoration.