Preheat the oven to 450 degrees Fahrenheit and line a large baking sheet with parchment paper or aluminum foil.
Lay the carrot and parsnip wedges in an even, single layer on the prepared baking sheet.
Whisk the salted melted butter, honey, thyme, nutmeg, and sea salt in a small mixing bowl until combined.
Remove 3 Tablespoons of the honey butter sauce and set to the side in a small bowl for now.
Slowly drizzle the rest of the sauce over the carrots and parsnips, then toss with your hands to coat.
Spread the carrots and parsnips over the prepared baking sheet in a single layer.
Cook the vegetables in the oven for 10 minutes, then flip them and bake for another 10 minutes or until they are soft enough for a fork to press through quickly.
Change the heat on the oven to broil and cook for another 3-5 minutes until the vegetables get blister spots and the honey is caramelized.
Remove the vegetables from the oven in a large serving dish and drizzle on the remaining sauce before serving, garnished with fresh thyme, optional. Serve hot.
Notes
To cut carrots into wedges: Trim off both ends. Cut them in half lengthwise. If they are thick, you may need to cut them into quarters lengthwise. Take each halved or quartered piece and cut diagonally into long wedges.