Preheat the oven to 400˚F. Line a large rimmed baking sheet with foil or a silicone mat.
Cut the carrots and parsnips into strips, approximately 2-inches in length. Cut thicker pieces in half lengthwise to make sure they are all approximately the same size.
Add the carrots and parsnips to the baking sheet. Drizzle with oil and season with salt, pepper, and fresh rosemary. Toss to coat. Spread the vegetables out in an even layer, making sure none of the pieces overlap.
Roast the carrots and parsnips for about 20 to 30 minutes, tossing every 10 minutes or so until fork tender. Remove from oven and set aside.
In a small bowl, whisk together melted butter, honey, balsamic vinegar, and red pepper flakes, if using.
Add the vegetables to a platter or serving bowl. Drizzle with honey glaze and toss to coat.
Serve immediately with a garnish of freshly chopped parsley, if desired.