Preheat oven to 400˚F (200˚C).
In a medium bowl, whisk together the olive oil, balsamic vinegar, garlic, oregano, salt, and pepper.
Cut the carrots into 2 inch (5 centimeter) pieces. If some of the carrots are too thick, cut them in half or even quarters lengthwise.
Place the carrots in a baking dish large enough to fit the pieces in a single layer, about 8 x 8 inches (20 x 20 centimeters).
Pour in the olive oil mixture and toss well to fully coat.
Roast the carrots in the preheated oven for 15 minutes.
Sprinkle the carrots with the grated Parmesan, toss again, and continue to roast until tender, about 15 more minutes.
Drizzle the melted butter over the carrots.
Serve immediately with a sprinkling of fresh parsley, and optionally a little more Parmesan, salt, and pepper.