Preheat the oven to 350°F (175°C).

In a mixing bowl, cream together ½ cup softened unsalted butter and 1 cup granulated sugar until light and fluffy.

Add 2 large eggs one at a time, mixing well after each addition.

Stir in ½ cup milk, 2 tablespoons elderflower cordial, 1 tablespoon lemon zest, and mix until combined.

In a separate bowl, whisk together 1 cup all-purpose flour, 1 teaspoon baking powder, and ½ teaspoon salt.

Gradually add the dry ingredients to the wet mixture, stirring until just combined.

Divide the batter evenly into cupcake liners in a muffin tin.

Bake for 15 minutes, or until a toothpick inserted into the center comes out clean.

Allow the cupcakes to cool completely.

For the frosting, cream together ¼ cup softened unsalted butter and 1 cup powdered sugar.

Mix in 2 tablespoons elderflower cordial, 1 tablespoon lemon juice, and 1 teaspoon lemon zest until smooth.

Frost the cooled cupcakes as desired.