Preheat oven to 180℃/356℉.
Grease and line a 20cm springform cake tin with baking paper.
Beat butter with lemon rind and vanilla extract until as light in colour as possible.
Add sugar. Cream sugar and butter until the mix looks light and fluffy.
Beat eggs and add slowly, beating well each time. (If using an electric mixture you can add the eggs one at a time unbeaten and mix on a moderate speed.)
Sift in half the flour and add half the milk. Mix lightly with a wooden spoon. Add remaining ingredients and mix lightly. If looking course, give the mix a very quick beating to smooth.
Bake for 30-35 minutes. Top of cake should feel firm to the touch and a skewer inserted into the thickest part of the cake should come out clean.
Cool cake 10 minutes in the tin before turning out.
For syrup, place water, sugar in a saucepan over medium heat. Bring to the boil and cook for 10 minutes to reduce. Take off heat and stir in vanilla. Allow to cool slightly before brushing cake with syrup and decorating.