Saute onions in butter and oil until onions are transparent, but not well browned. When tender, turn heat to lowest point and sprinkle with flour, stirring vigorously. Pour into Dutch oven and stir in broths. Heat thoroughly and divide among 8 oven-proof bowls. Float a slice of bread atop each serving. Mix equal parts of cheese to smooth paste and spread over bread. Place all bowls on oven rack 4 from broiler heat and broil until cheese melts. Serve at once. Leftover soup freezes well up to 6 months.