Melt butter in large pot. Remove from heat. Add parsnips and toss to coat. Sprinkle with salt and pepper.
Preheat oven to 375F degrees. Spray large rimmed baking sheet with nonstick spray. Using slotted spoon, transfer parsnips to prepared sheet. Reserve pot with butter.
Roast parsnips until tender, tossing occasionally, about 45 minutes. Add lemon juice, lemon peel, and nutmeg to reserved pot. Add parsnips. Toss over medium heat until coated with lemon butter, about 2 minutes. Season with salt and pepper.