Preheat the oven to 400℉. Line a baking sheet with aluminum foil and set aside.
Peel and trim the carrots and parsnips. If any of the veggies are thicker than the width of your thumb, cut them in half lengthwise. You want all the veggies to be roughly the same thickness so they will all cook evenly. Transfer the carrots and parsnips to the prepared baking sheet.
Drizzle the carrots and parsnips with olive oil, honey, paprika, salt, pepper and cayenne pepper. Toss until the vegetables are evenly coated. Spread the carrots and parsnips evenly into one layer on the baking sheet.
Cover with aluminum foil and bake for 15 minutes. Remove aluminum foil, flip the vegetables, and bake for an additional 10-15 minutes, until the vegetables are fork-tender.
Remove from the baking sheet and serve immediately.