Preheat the oven to 180°C (350°F).
Grease a baking dish with butter and set aside.
In a large bowl, crumble the soda bread into small pieces.
In another bowl, whisk together milk, eggs, brown sugar, vanilla extract, cinnamon, and salt until well combined.
Pour the custard mixture over the crumbled soda bread, ensuring all pieces are well soaked.
Transfer the mixture to the prepared baking dish.
Bake in the preheated oven for 40-50 minutes or until the top is set and golden brown.
Allow the pudding to cool for about 10 minutes before serving.