Preheat oven to 400˚F. Lightly oil a rimmed baking sheet.
In a small saucepan, combine the olive oil and garlic over medium heat. Cook just until the garlic is fragrant, about 1 minute. Remove from heat.
Arrange the peeled carrots on the prepared baking sheet in a single layer. Evenly drizzle with the garlic oil. Sprinkle with salt, pepper, and the oregano.
Roast in preheated oven for 15 minutes. Flip the carrots over, sprinkle with Parmesan and cook for another 10-15 minutes or until the carrots are tender.
Drizzle the melted butter over the carrots and top with parsley. If desired, add a little more salt, pepper, and Parmesan. Serve immediately.