Prepare the Dough: In a large mixing bowl, combine the plain flour, caster sugar, and lemon zest. Add the chilled, cubed butter and rub it into the flour mixture using your fingertips until it resembles fine breadcrumbs and begins to form a dough.
Form and Chill the Dough: Bring the dough together gently, form it into a ball, and flatten slightly. Cover with plastic wrap and place in the refrigerator for 30 minutes to allow it to firm up.
Roll and Cut the Cookies: Preheat the oven to 350°F (180°C) and line a baking sheet with parchment paper. Roll the dough out on a floured surface to about ¼ inch (6 mm) thickness. Use a round cookie cutter to cut out cookies, placing them on the prepared baking sheet.
Bake: Bake for 10-12 minutes, or until the edges are just starting to turn golden. Allow the cookies to cool on the baking sheet for a few minutes, then carefully move them to a wire rack to cool completely.
Prepare Buttercream Filling: In a mixing bowl, beat the softened butter until creamy. Gradually add the icing sugar, mixing until smooth. Add the lemon juice, elderflower cordial, and milk, beating until light and fluffy. Set aside
Assemble the Sandwiches: Spread a small amount of lemon curd on the underside of half of the cookies. Pipe or spread the elderflower buttercream over the lemon curd, then top each with another cookie to form a sandwich.
Drizzle with White Chocolate: Using a spoon or piping bag, drizzle the melted white chocolate over the tops of the sandwich cookies.