Slow cooking produces a rich onion flavor; the sugar colors onions and broth brown.
Melt butter in soup kettle. Add oil, stir in onions, and cook, covered, over low heat 20 minutes. Remove cover, increase heat slightly, sprinkle onions with sugar, and cook, stirring frequently, 20 minutes longer. Sprinkle onions with flour, stir until smooth. Gradually add hot stock, stirring constantly until smooth. Simmer, partially covered, 20 minutes. Garnish with grated Parmesan or baked cheese. To garnish with baked cheese: Preheat oven to 350 degrees, pour hot soup into oven-proof bowls, and set on baking sheet. Place a round of toasted French bread on top of each bowl and sprinkle with a thick layer of grated Swiss cheese, or a mixture of Swiss and Parmesan. Dot cheese with butter and bake 15 minutes. If desired, after baking, run bowls under broiler for 1 or 2 minutes to brown cheese.