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Butter two 20cm loose-bottomed cake tins and line the base and sides with baking parchment. Heat the oven to 180C/160C fan/gas 4. Tip the butter and caster sugar into a stand mixer and beat until pale and fluffy. Or, do this using an electric whisk. Add the eggs, one at a time, beating between each addition.
Add the flour, baking powder and a pinch of salt and mix again, then the yogurt. Zest the two lemons, add this and mix until everything is fully combined. You may need to scrape the sides of the bowl as you go.
Divide the cake batter between the prepared tins and smooth the surfaces with a spatula. Bake for 30 mins, or until a skewer inserted into the middles comes out clean. Cool in the tins for 10 mins, then transfer to a wire rack to cool fully. Once cool, the cakes can be wrapped and frozen for up to three months. Defrost overnight before icing.
For the candied lemon peel, use a vegetable peeler to remove the peel from the remaining lemon in long, thin strips. Use a small, sharp knife to cut the white pith away from the peel, then cut it into thinner strips. Put 50g of the caster sugar in a small pan with 100ml water. Juice all three lemons and pour into the pan. Bring the mixture to the boil, reduce to a simmer and cook for a few minutes until the sugar has dissolved. Tip in the strips of lemon peel, then return to the boil, reduce the heat to a simmer again and cook for 5 mins until the peel is soft. Tip the remaining 25g sugar into a bowl. Remove the lemon peel from the syrup using a fork and add to the bowl of sugar. Shake the bowl gently to coat the strips of peel, then shake off the excess and arrange the candied peel on a plate or baking tray in a single layer to dry, about
30 mins. Once set, the candied peel will keep in an airtight container in a cool place for six months.
Spoon 3 tbsp of the lemon syrup over each of the cooled sponges. For the icing, beat the butter in a stand mixer until soft and creamy, or do this using an electric whisk. Add half the icing sugar and half the soft cheese, then beat again. Add the rest of the icing sugar and soft cheese and most of the freeze-dried strawberry powder (reserving 1 tsp for decorating later), and beat until well-combined.
Hull and finely chop 200g of the strawberries. Put one of the sponges on a cake stand or plate and spread over a generous amount of icing. Scatter evenly with some of the chopped strawberries and put the second sponge on top. Spoon the rest of the icing over the top and use a palette knife to spread it all over the top and sides, smoothing and swirling it as you go. Thinly slice five or six strawberries of a similar size, then arrange these around the base of the cake, with the pointed ends facing upwards. Cut half the remaining strawberries in half, leaving the rest whole with their stalks intact, and pile all of these on top of the cake. Scatter over the candied lemon peel, reserved freeze-dried strawberry powder and the popping candy, if using. Best eaten within a day, but will keep chilled for up to two days.