Trim the ends off each onion then halve lengthwise. Remove peel and finely slice into half-moon shapes. Set electric skillet to 300 degrees and add butter. Once butter has melted add a layer of onions and sprinkle with a little salt. Repeat layering onions and salt until all onions are in the skillet. Do not try stirring until onions have sweated down for 15 to 20 minutes. After that, stir occasionally until onions are dark mahogany and reduced to approximately 2 cups. This should take 45 minutes to 1 hour. Do not worry about burning.
Add enough wine to cover the onions and turn heat to high, reducing the wine to a syrup consistency. Add consomme, chicken broth, apple cider and bouquet garni. Reduce heat and simmer 15 to 20 minutes.
Place oven rack in top 1/3 of oven and heat broiler.
Cut country bread in rounds large enough to fit mouth of oven safe soup crocks. Place the slices on a baking sheet and place under broiler for 1 minute.
Season soup mixture with salt, pepper and cognac. Remove bouquet garni and ladle soup into crocks leaving one inch to the lip. Place bread round, toasted side down, on top of soup and top with grated cheese. Broil until cheese is bubbly and golden, 1 to 2 minutes.