Sauté onions in butter and oil until onions are transparent, but not well-browned. When tender, turn heat to lowest point.

Sprinkle with flour, stirring vigorously.

Pour into Dutch oven.

Stir in broths.

Heat thoroughly.

Divide among 8 oven-proof bowls.

Mix equal parts of cheese to a smooth paste. Spread over bread.

Float a slice of bread atop each soup serving.

Place all bowls on oven rack 4-inches from broiler heat.

Broil until cheese melts. Serve at once.

Leftover soup freezes well up to 6 months.