Gratin of Cabbage

Ingredients:

2 tablespoons unsalted butter, plus extra for greasing the pan
1 tablespoon vegetable oil
1 medium head cabbage (about 1-1/2 pounds), quartered, cored, and sliced into 1/2-inch-wide pieces
2 scallions, roughly chopped
2 carrots, grated
Kosher or sea salt
Freshly ground black pepper
1-1/2 cups mild chicken stock
1/2 pound grated cheese (Parmigiano reggiano, Swiss, or brie)