Preheat the oven to 400˚F. Line a rimmed baking sheet with parchment paper.
Place potatoes and carrots in a large bowl. Add butter, garlic, oregano, salt, thyme, and pepper. Gently toss to coat the vegetables.
Spread the vegetables in a single layer on the prepared baking sheet.
Bake for 30 to 40 minutes, until fork tender. Remove from the oven and add to serving bowl or platter. Garnish with parsley. Serve warm.