Put a heavy stock pot over medium heat. Add the oil and butter. Reserving a quarter of an onion, slice the rest of the onions and add them to the pot. Cook, covered, roughly 15 minutes until they are translucent.
4-5 Yellow Onions, 1 Tbsp Oil, 2 Tbsp Butter
Add the sugar and pinch of salt and cook, uncovered, stirring often until the onions have turns a dark caramel color. This takes 45 minutes to an hour. Note: pay close attention to the onions once they start to darken, or the edges will start to char. It won't be the end of the world, but it isn't perfect.
1/2 tsp Sugar, 1 Pinch Salt
Once caramelized, remove half the onions and add the flour to the remaining onions in the pot. Cook for 2-3 minutes, until the flour turns golden.
1 1/2 Tbsp Flour
Add a cup of stock (or broth) to the pot and scrape the cooked-on bits from the bottom of the pot. Add the rest of the stock (or broth), the 1/2 cup wine, cover the pot, and simmer the soup for 30 minutes.
4 C Beef Stock or Broth, 1/2 C Dry White Wine
While the soup simmers, prep the grilled cheese. Stack the two sandwiches in this order:bread, two slices swiss cheese,half of the reserved caramelized onions, half the parmesan,bread 9 Slices Swiss Cheese, 4 Slices Bread, 2 Ounces Parmesan Cheese
Add a thin application of mayo to the outside, on both sides, of each sandwich and place them in a cold skillet. Set the burner to medium heat. I like to start the pan cold to give the cheese inside the sandwich more time to melt before the bread toasts. 1 Tbsp Mayonnaise
Once the sandwiches are grilled to a golden brown on each side, set them aside for at least five minutes to allow the cheese to set a little. By doing this, they will still be gooey without being runny.
When the soup has simmered for 30 minutes, grate (or blend) the reserved 1/4 raw onion and add it to the soup. Stir in the last slice of swiss cheese and the optional cognac, and add salt and pepper to taste.
2-3 Tbsp Cognac
Serve the sandwiches on a plate with a side of soup in bowls. Garnish the soup with grated parmesan and fresh cracked black pepper.