Heat oven to 350 degrees Butter a large 2-quart gratin or casserole pan. In a large saute pan over medium heat, melt the butter with the oil, then the cabbage and scallions, and carrots. Season generously with salt and pepper, and cook, stirring, until the cabbage is nicely wilted and just beginning to brown in spots, about 10 minutes. Add the stock and adjust the heat to a simmer, and cook about 5 minutes. Transfer the to the prepared dish. Tightly cover with foil, and bake for 30 minutes. Remove the foil, and continue to bake until the liquid is mostly evaporated, about 20 minutes more. Then remove the dish from the oven. Sprinkle with cheese, increase oven temperature to 375, return the dish to the oven, and cook until the cheese is thoroughly melted, about 10 minutes. You can serve now, but for extra deliciousness, put under the broiler for 2 minutes.