Make the topping: Place potatoes and parsnips in a medium sauce pan, cover with water and bring to a simmer. Cook until fork tender, about 20 minutes. Drain, reserving 2 cups cooking liquid. Pass potatoes and parsnips through a ricer or mash, Stir in yogurt and 3/4 teaspoon salt. Season with pepper.
Make the filling: Heat oil in a medium skillet over medium heat. Cook onion, celery, carrots and garlic, stirring, until tender, 10 to 12 minutes.
Add meat, cook, breaking up any large pieces, for 5 minutes. Stir in 1 1/2 teaspoons salt, the thyme, and chili powder and season with pepper. Whisk together cornstarch and reserved 2 cups cooking liquid and add to turkey. Boil for 1 minute. Stir in peas. Transfer to a 2-quart baking dish and top with potatoes. Bake until bubbling and top is browned, 35 minutes. Serves 8 (Martha Stewart)