Make the madeleine batter. Add the caster sugar and eggs to a large bowl (ideally a stand mixer) and whisk on high speed for about 7 minutes, until thick and holds a trail. Meanwhile, melt the butter in very short 20 second bursts in the microwave so that it is of liquid consistency but not too hot. Then weigh the flour and baking powder in a separate bowl. Grate the lemon rind.
When the sugar and egg mixture is thick and holds a trail, pour in the milk, then sift in the flour and baking powder. Add the lemon rind and vanilla bean paste, and then whisk until just incorporated. Pour in the cooled melted butter, and whisk again until just combined. Do not over mix.
Cover with cling film and place in the freezer for 30 minutes. Melt a little extra butter and use this to grease a madeleine tin. Then place the madeleine tin in the freezer too. At this point, preheat the oven to 220C (fan).
Meanwhile, make the lemon dip. Whisk together the lemon juice and the icing sugar, until the consistency is smooth and runny, but is still opaque when coating the back of a spoon. Add a little more lemon juice/icing sugar until you have the correct consistency.
Put your madeleines into the oven, piping in a small amount of batter to each section of your tray. The batter shouldn’t fill the tray, there should be small gaps around the edges to allow your madeleines to rise in the oven.
Set aside a small amount, and add more icing sugar to this until it of piping consistency, then transfer to a piping bag ready for later. Add green food dye to the remaining larger amount. Pour the green icing into a wide-brimmed cup (choose one suitable for dipping the madeleines into), and cover with cling film for now.
When the madeleines are cool, dip one by one (scalloped end first) into the green lemon icing. Aim to have just under half of the madeleine’s surface area covered. Leave the madeleines to set on a wire rack.
When the green icing has set, use the white icing in the piping bag (set aside earlier) to decorate with white lines.