In a large saucepan, melt the butter over low heat. Add the onions and sprinkle with salt. Stir to coat the onions in the butter. Cover and cook for 30 minutes, stirring occasionally. Remove the lid and stir in the thyme and the cognac. Raise the heat slightly and cook onions, stirring often until they turn a deep caramel color, about an hour. Watch them carefully! You don’t want them to burn.
Add the stock, thyme sprigs and pepper. Bring to a boil and then reduce heat to a simmer. Cover and cook for 30 minutes.
Meanwhile, toast the bread slices. This can be done in a toaster or in the oven. In the oven, place bread slices on a baking pan and cook at 350° F for 10 minutes until golden and crispy.
Remove the time sprigs from the soup. Ladle the soup into 4-6 ovenproof soup bowls or large ramekins (the number of bowls you use will depend on their size). Sprinkle a bit of cheese on top of the soup and place a slice of bread on top of the cheese. Top the bread with more cheese.
Place the bowls on a baking sheet and place on the middle rack in the oven and broil for 2-3 minutes until the cheese is melted and bubbly and starting to brown in places.
We like to make some extra cheese toasts to serve on the side. You can make extra slices of toasted bread and top them with grated cheese. Broil them alongside the soup for 2-3 minutes until cheese is bubbly and starting to brown.
Serve immediately.