Preheat your oven to 425°F. Scrub potatoes and cut them into large bite-size pieces, about 2-inches.
Place potatoes on the baking sheet and drizzle with 2 tablespoons of the oil and ¼ teaspoon salt. Toss until well-coated. Arrange potatoes so they are evenly spaced over the tray.
Cover with foil and bake for 15 minutes. While your potatoes bake, peel and trim the tops of your carrots and slice them into 2-inch chunks. For larger carrots, slice the thick upper part in half lengthwise before cutting into pieces.
Remove the potatoes from the oven and raise the temperature to 475°F.
Remove and discard the foil. Add carrots to the tray and drizzle the remaining 1 tablespoon of olive oil, oregano and remaining ¼ teaspoon of salt over the top. Toss until well-coated.
Arrange the vegetables so they are evenly spaced on the tray, preferably with a cut-side down, and bake uncovered for 30 to 35 minutes, shaking the pan once halfway through to move everything around, until the carrots are tender.
Remove from the oven, add additional salt if needed, and enjoy!