1. Preheat oven to 375° F. Begin mashed vegetables: Place cut potatoes and celery root in large pot; add cold water till covered. Bring to boil, salt generously, cover and simmer until potatoes are easily pierced with fork (10-12 minutes). Drain well; return to pot off the heat to dry.
2. Begin the stew: Heat 1 TBSP oil in large skillet over medium-high heat. Add onion, garlic, mushrooms, and thyme; cook, stirring occasionally, until mushrooms are golden and soft (about 8 minutes). Remove and spread along bottom of a 2-quart casserole dish. Heat 1 TBSP oil in the same skillet; add the beef or lamb, carrot, rosemary, and nutmeg; cook until beef is brown and carrot is tender (about 8 minutes). Stir in tomato paste. Layer over mushroom-onion mixture.
3. Finish the mashed veggies: Pass potatoes and celery root through a food mill into a bowl, adding butter as you go. Stir in yogurt and milk for a purée. Season with salt and pepper.
4. Swirl mashed potatoes and celery root over stew with back of a spoon; sprinkle on cheese. Bake until cooked through and cheese is golden brown (15 minutes). Serve warm.