Preheat oven to 400 degrees F (200 degrees C). Combine chicken broth and butter in a 9x13-inch baking dish; place dish in oven to melt butter while oven preheats.
Toss baking potatoes, sweet potatoes, celery root, parsnips, salt, and black pepper together in a bowl. Pour into prepared baking dish and stir to coat vegetables with broth mixture. Cover the baking dish with aluminum foil.
Roast vegetables in the preheated oven for 40 minutes. Uncover the baking dish and discard aluminum foil. Pour heavy whipping cream over vegetables and sprinkle Gruyere cheese over the top. Continue baking until vegetables are tender and cheese is melted and golden, about 30 minutes. Cool for 10 minutes before serving.