Preheat oven to 450 degrees. Peel and cut parsnips as directed above; then cut on a diagonal into 1/2-inch-thick pieces.
On a large rimmed baking sheet (or two smaller baking sheets), toss parsnips and sweet potatoes with oil; season generously with salt and pepper. Spread in a single layer. Roast until tender and golden, tossing once or twice, about 30 minutes. Transfer to a large bowl.
In a small bowl, stir together maple syrup and mustard. Pour over vegetables; toss to coat. Sprinkle with parsley, if desired. Serve immediately.
To cut parsnips: Trim tops and bottoms; peel, and slice in half crosswise to separate thick and narrow parts. Halve or quarter thick parts lengthwise, until all parsnip pieces are roughly the same size (this ensures even cooking).