In a saucepan, heat the oil and cook the onion and carrot until the vegetables are soft.
Add the fumet, milk, thyme, salt and pepper, and then bring to a boil while stirring. Lower the heat and add the potato cubes. Simmer on low heat about 20 minutes or until the potatoes are soft.
Add the corn and the fish cubes and continue cooking about 5 minutes, or until the fish is cooked. Adjust the seasoning, as needed.
In a small bowl, mix the cornstarch in water until it dissolves well, and then add this mixture to the soup, stirring constantly. Bring to a boil. The soup will thicken.
