Lightly grease a 20 x 30cm loose-bottomed cake tin with a little of the melted butter, then line with baking parchment. Heat oven to 180C/160C fan/gas 4. Put the eggs and sugar in a large bowl, and whisk with an electric hand whisk until the eggs are pale cream, doubled in volume and hold a ribbon pattern on top of the mixture for 3 secs. Drizzle the cooled butter around the edge of the bowl, and sift the flour and baking powder over the top with a pinch of salt. Use a large metal spoon to fold everything together until just combined, being careful not to knock out too much air. Carefully pour the mixture into the prepared tin, level the surface, and bake for 25 mins until golden and a skewer inserted to the centre of the cake comes out clean. Leave to cool for 10 mins in the tin, then carefully slide out onto a wire rack and leave to cool completely.
Meanwhile, make the buttercream and syrup. Put the poppy seeds in a pan and toast for a few mins until aromatic, then leave to cool completely. For the syrup, put the ingredients in a saucepan, bring to a simmer, bubble for a few mins until the sugar has dissolved, then leave to cool. For the buttercream, beat the butter and icing sugar together until smooth, add the lemon zest, lemon curd, milk and cooled poppy seeds.
When the cake is totally cool, carefully slice into 3 thin layers. Reassemble the cake in the tin, flipping what was the top into the tin to make the bottom layer. Spoon over a third of the syrup, then spread over half the buttercream. Top with the middle layer of the cake, more syrup and the remaining buttercream. Top with the final sponge, flat-side up, and drizzle over the remaining syrup.
Mix the icing sugar with enough lemon juice to make a thick but spreadable icing. Colour the icing with a little food colouring, then pour over the top of the cake, easing it to cover the entire surface. Leave in the tin to set for at least 2 hrs.
When you’re ready to serve, carefully remove the cake from the tin. Cut off the edges with a long serrated knife, then cut into 24 little cakes. Will keep in a sealed container for up to 3 days.