Fill a large pot with 1 inch of water and fit with a steamer basket; bring the water to a boil. Place the carrots in the basket, cover, and steam until tender, 6 to 8 minutes; drain and toss with the butter, oregano, and ½ teaspoon salt.
Meanwhile, rub the tilapia with the blackening seasoning. Heat the oil in a large nonstick skillet over medium-high heat. Cook in batches until cooked through, 2 to 3 minutes per side, adding more oil to the pan if necessary. Serve with the carrots and corn bread.