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Heat oven to 180C/160C fan/gas 4. Butter 2 x 20cm sandwich tins and line the bases with baking parchment. Zest 2 lemons, then squeeze their juice into a separate bowl. Put 200g butter, the caster sugar, eggs, courgettes, poppy seeds, vanilla and lemon zest into a mixing bowl. Beat to a creamy batter. Stir in 1 tbsp lemon juice, the flours, baking powder and ¼ tsp salt. Spoon the mix into the tins, then bake for 25 mins or until risen, golden and springy in the middle.
Make a drizzle by mixing another tbsp lemon juice with 25g icing sugar. Put the remaining icing sugar and butter into a bowl, add the soft cheese, remaining lemon juice (about 2 tbsp) and grate in the final lemon’s zest. Beat to make a creamy, smooth frosting.
When the cakes are ready, cool for 15 mins in their tins, then turn onto a cooling rack. Prick several times with a cocktail stick, spoon over the drizzle and cool completely. Can be frozen at this stage for up to 1 month. Put one cake onto a serving plate and spread with just under half the frosting. Spread over the lemon curd, if using. Top with the second cake, spread the remaining frosting over the top and sprinkle with poppy seeds.