Preheat oven to 400 F. Line 2 baking sheets with parchment paper.
Peel carrots and parsnips. Trim the ends, and cut each in half lengthwise.
Divide carrots and parsnips between the two pans. I like to mix them on each pan.
In a small bowl, whisk together honey, olive oil, rosemary, garlic, vinegar, mustard, salt, and pepper.
Drizzle sauce over the carrots and parsnips, dividing it between the two pans. Gently stir to coat the vegetables.
Roast for 30 minutes in the preheated oven - stirring every 10 minutes - or until fork tender and starting to brown.
Taste, season with additional salt and pepper if desired, transfer to serving dish.
Finely chop some parsley, scatter over the roasted vegetables, and serve hot.