Heat oven to 160C/140C fan/gas 3. Grease and line a 20cm loose-bottomed cake tin. Beat the butter and sugar with an electric whisk until pale and creamy. Add the eggs one at a time, then add the lemon zest and juice and vanilla extract. Fold in the flours with a metal spoon until well mixed. Transfer to the cake tin, smooth the top, then bake for 50 mins until risen and golden.
To make the syrup, mix the lemon juice with the pomegranate juice, caster sugar and vanilla, then heat gently until the sugar dissolves. Increase the heat and reduce slightly until syrupy. Remove from the heat and cool slightly, then tip in the pomegranate seeds.
Remove the cake from the oven. Allow to cool for a few minutes before poking holes all over it with a skewer and pouring over the pomegranate syrup. Enjoy warm or cool completely in the tin.