Preheat oven to 350 degrees. Lightly butter a 3-quart baking dish. Place the celery root, potatoes, and fennel in a large bowl and toss well.
In a large measuring cup, combine the flour, salt, and pepper. Whisk in the milk.
Layer 1/3 of the vegetables in the prepared baking dish. Sprinkle with 1/3 of the cheese. Repeat layering, reserving the last 1/3 of the cheese.
Pour the milk mixture over all, pressing the vegetables to coat them. Sprinkle the remaining cheese on top. Bake for 1 hour, or until the vegetables are very tender.