Melting Onions

Position rack in upper third of oven. Preheat to 450°F.

Toss onions, oil, butter, sage (or thyme), salt and pepper in a large bowl. Spread in a 9-by-13-inch metal baking pan (don't use glass or ceramic, which might shatter). Roast, turning once, until browned on both sides, 30 to 35 minutes total.

Turn the onions again and carefully add broth to the pan. Continue roasting until the broth is reduced and the onions are very soft, 15 to 20 minutes more.