Preheat oven to 450 degrees F.

With a sharp knife trim root end of each onion flat so that it is still intact but will stand on end. Standing each onion on its root end, cut parallel vertical slices at 1/4-inch intervals into but not through onion, stopping about 3/4-inch above root end. Rotate each onion 90 degrees and cut parallel vertical slices in same manner to form a crosshatch pattern, keeping onions intact.

In a lightly buttered shallow baking dish large enough to let onions open, or "flower, " put onions, root ends down, and sprinkle with sugar and salt to taste.

In a small saucepan heat broth and butter over moderately high heat until butter is melted and pour over onions. Cover onions with foil and roast in middle of oven 45 minutes, or until tender. Remove foil and roast onions, basting occasionally, 30 to 45 minutes more, or until golden. Onions may be made 1 day ahead and chilled, covered. Reheat onions before serving.