In a covered 4 litre saucepan, cook the thinly sliced onions slowly with the butter and 1 Tbs oil for about 15 minutes. Keep covered, stir occasionally. Uncover and increase heat to moderate. Add sugar and saute onions until golden brown, about 30 minutes. Sprinkle onions with flour and stir over heat for 2 or 3 minutes. Blend in hot broth and vermouth, season to taste. Simmer partly covered for 1 hour. Place bread slices in a 350 oven for 15 minutes. Remove and baste each slice with half tsp oil and rub with cut garlic clove. Return to oven for about 15 minutes. Before serving, add cognac to soup and divide into 4 ovenproof bowls. Sprinkle half cup of cheese in soup. Float slices of bread on top of soup and sprinkle with the remaining cheese. Bake in 325 oven 15 to 20 minutes until hot. Set under broiler for 2 or so minutes until golden brown.