Preheat the oven to 350°F (175°C) and line a cupcake pan with cupcake liners.

In a large bowl, cream together ½ cup of softened unsalted butter and granulated sugar until light and fluffy.

Add eggs one at a time, mixing well after each addition.

Stir in buttermilk, lemon juice, lemon zest, baking powder, baking soda, and salt.

Gradually add in the all-purpose flour, mixing until just combined.

Fill cupcake liners with the batter until about two-thirds full.

Bake for 15 minutes or until a toothpick inserted comes out clean. Allow to cool.

For the frosting, cream together the remaining ½ cup of softened unsalted butter and powdered sugar.

Mix in 2 tablespoons of lemon juice, lemon zest, and milk (if needed for consistency) until smooth.

Once cupcakes are cool, frost them with the lemon frosting.