In a large, heavy-bottomed Dutch oven, add the butter and oil, then the sliced onions. Cook slowly, with the lid on, for about 15 minutes. Stir occasionally.
Remove the lid, turn the heat up to medium, add the salt and sugar, and stir often for about 40 minutes (mine took 45 min), until the onions are a deep golden brown.
Add the flour and continue to cook and stir for another 3 or 4 minutes. Remove from heat and add the stock/water/bouillon and wine.
Add salt and pepper to taste and return to the cooktop, and simmer for an additional 30 to 40 minutes. Just before the soup is ready, preheat the oven to 350℉/ 175℃.
When the soup is ready, add the brandy/Cognac, if using and check for seasoning; ladle it into ovenproof bowls, and GENIUS SERVING TIP - top with the cubes of toasted bread - not an entire slice. It's so much easier to eat this way!
Sprinkle the cheese on top of the toast, as desired.
Repeat to make 6 bowls, then place them on a tray and put into the center of the oven for about 15 minutes.
Reset the oven to broil (grill) and move the tray of bowls closer to the top to get a nice golden color on the cheese, which should be watched carefully as it can burn quickly.
Serve immediately.