Melt the dripping in a hot saucepan. Add the oatmeal and cook for 2-3 minutes then stir in the corned beef, breadcrumbs and raw carrots.
Stir in the vegetable stock until well combined.
Grease a pudding basin and spoon in the mixture.
Fold a large piece of aluminium foil in half and grease one side with butter. Wrap the pudding in the greased foil, greased side facing into the pudding. (Pleat the foil a few times as you wrap it to allow room for the pudding to expand.) Secure the foil to the rim of the pudding basin with string.
Place the wrapped pudding into a large steamer. (Alternatively, place the wrapped pudding into a large pan, pour in enough boiling water to reach halfway up the sides of the basin, then cover the pan with a lid.) Steam the pudding over a medium heat for 1 hour 30 minutes, or until cooked through, topping up the steamer with boiling water as necessary. (NB. The pudding is cooked through when a skewer inserted into the centre comes out clean.)