Preheat the oven to 180°C and grease a baking dish. Cream the butter and sugar together until light and fluffy, then add the eggs one at a time and mix well. Stir in the vanilla essence. Add the flour and salt, alternating with the milk, until you have a smooth batter.
Pour the batter into the prepared baking dish and bake for about 30–40 minutes until golden and cooked through.
While the pudding is baking, prepare the syrup by combining the boiling water, sugar, butter, apricot jam, and vanilla essence in a saucepan. Stir until the sugar has dissolved and the butter has melted.
Pour the hot syrup over the freshly baked pudding while it is still warm. Allow it to soak in before serving.
Serve warm with custard, cream, or ice cream.