Heat oven to 180C/160C fan/gas 4. Line the base and sides of a 20cm square tin with baking parchment (the easiest way is to cross 2 x 20cm strips over the base). Beat the butter, caster sugar, flour, almonds, baking powder, eggs, vanilla and the lemon zest and juice from ½ lemon with an electric whisk until smooth. Scrape into the tin and bake for 25-30 mins until a skewer poked in comes out clean. Let cool.
Turn out onto a wire rack, trim edges and slice into 16 squares. Tip the granulated sugar onto a plate. Pour remaining lemon juice into another shallow dish. Very, very quickly, dip all sides of the cake squares, one-by-one, into the juice, then quickly in the sugar. Sit on a wire rack to set and crisp.