Preheat the oven to 200C/180C Fan/Gas 6. Line/Grease an 8" square tin.
In a large bowl, or the bowl of a stand mixer, cream together the butter and sugar on a high speed for 3-5 minutes. Add the eggs, one at a time and the vanilla.
Add in the flour and baking powder and fold together until combined. Add the milk. Pour into the lined tin and bake 25-30 minutes, until golden on top and a skewer inserted comes out clean.
While the cake is baking, make the syrup by bringing the water, sugar and vanilla to a boil over a medium heat. Once the sugar has dissolved, turn off the heat and let the syrup cool.
When the cake has cooled, ensure the top is flat (cut across if not - scraps can be eaten). Spread the syrup over the two halves that will be sandwiched together (I use what was the base to form the top as it is flat).
Spread the jam over the top of one of the cake halves and sandwich together. Brush over a little more of the syrup if any remains, dust with a little icing sugar, and slice into 5-6 fingers!