Preheat oven to 400°F and line a large rimmed baking sheet with parchment paper.
Give vegetables a good scrub and thoroughly dry.
Peel carrots and parsnips with a vegetable peeler. Cut carrots and parsnips in half lengthwise. If vegetables are too large, cut them into quarters so pieces are uniform in size.
In a large bowl, toss carrot and parsnip pieces with the olive oil and kosher salt. Place coated vegetables in a single layer on parchment-lined rimmed baking sheet.
Roast carrots and parsnips until tender and caramelized, about 30-35 minutes, tossing every 10 minutes to ensure even roasting.
Melt the butter in a small saucepan over medium heat, and then add the honey, stir to combine.
To serve, transfer roasted vegetables to a serving dish, drizzle with honey glaze over, and toss to coat.