Heat the oil in a large saucepan. Peel, wash and slice the potatoes and sauté in the hot oil for about 2 minutes. Press the garlic through a press and cook with it.
Add the wheat flour and sauté briefly. Pour in the milk and vegetable stock and let it boil until it thickens. Add the corn and simmer everything together for about 20 minutes. Add the grated cheese and let it melt. Season to taste with the dried basil and a little salt and pepper.