Preheat oven to 425°F (220°C). Line a baking sheet with parchment paper.
Trim ends of carrots and parsnips. Slice lengthwise into even pieces.
In a small bowl, whisk together honey, melted butter, and olive oil.
Place vegetables on the baking sheet and drizzle with the honey mixture. Toss well to coat.
Spread evenly in a single layer. Sprinkle with salt, pepper, and thyme.
Roast for 30–35 minutes, flipping halfway, until edges are caramelized and vegetables are fork-tender.
Serve hot, garnished with more thyme or chopped parsley if desired.