Preheat the oven to 170°C/150°C fan/325°F/gas 3. Grease and line three 15 cm/6 in round cake pans.
Boil the peas for a few minutes, drain, refresh under cold water and drain again. Puree with a hand blender until smooth. Set aside.
In a large bowl, cream the butter and sugar with an electric mixer until light and fluffy. Beat in the eggs well, one at a time, then beat in the cooled pea puree, vanilla, lemon zest and juice. Sift in the flour, baking powder and salt, and stir gently to combine.
Divide the batter among the prepared pans, then bake for 25 minutes, or until a skewer inserted in the middle comes out clean. Leave to cool in the pans for 10 minutes, then turn out onto a wire rack to cool completely before icing.
to make the lemon buttercream
In a large bowl, cream the butter with an electric mixer until fluffy. Add the icing sugar and beat until combined. Beat in the lemon zest and a little of the juice. If necessary, add more icing sugar or a teaspoon of milk to reach the consistency of thick frosting. Store in the fridge until ready to use.
Sandwich together the cake layers with a little of the buttercream. Cover the cake in the remaining buttercream and decorate with pea shoots and lemon zest.