Heat the oil in a medium saucepan over moderate heat. Add the onion and garlic and cook for 7 minutes or until the onion is soft.
Add the baking potatoes, red potatoes and sweet potatoes, stirring to coat. Add the stock, 2 cups water, the thyme and a pinch of salt, and bring to the boil. Reduce to a simmer, cover and cook for 25 minutes or until the red potatoes and sweet potatoes are tender, and the baking potatoes are soft and creamy.
Stir in the milk and corn and simmer for 4 minutes or until the corn is heated through. Stir in the parsley just before serving.
Did you know?
Greenish skin – or sprouts – on a potato signal elevated levels of solanine, a bitter-tasting compound that is a natural component of this vegetable. It's best to discard any potatoes that have a greenish tinge or more than one or two sprouts. It would take a lot of solanine to make you ill, but it's best to avoid it. * To flavour potatoes without adding fat, toss a few garlic cloves, onion slices or fresh herbs into the cooking water.