Step 1Peel the celery root. Cut off the knobby top and bottom. Set the root upright on a cutting board and trim away the tough outer peel with a chef's knife. Cut into roughly 1-inch cubes and place in a large saucepan with cold water.
Step 2Peel and cube the potatoes and add the potatoes and the garlic to the saucepan. Season the water liberally with salt and bring to a boil. Reduce the heat to a simmer and cook until the vegetables are tender enough to be crushed with a fork, 20 to 25 minutes.
Step 3Drain the vegetables and empty them into a food mill fitted with a fine disk. Turn the crank, pressing the vegetables through the disk into a clean saucepan underneath. You may need to reverse the blade a time or two to clear any tough fibers that are caught in the disk. Scrape the puree on the underside of the disk into the saucepan. Depending on the size of your food mill, you may need to puree the vegetables in two batches to accommodate them comfortably.
Step 4Place the saucepan over medium heat and stir the ground vegetables with a wooden spoon until they form a smooth paste. The heat is also drying excess moisture out of the vegetables; stop when a dry film begins to form on the bottom of the pan. Beat in the butter and when it is thoroughly incorporated, beat in the whipping cream to make a silky puree.
Step 5Season the puree to taste with more salt if necessary, white pepper and a pinch of nutmeg and spoon it into a serving bowl. If you like, place a knob of butter on top to melt into the mixture.