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Step 1
Slice the onions into ¼-inch thick slices. Add the sliced onions to a large soup pot with olive oil. Cook the onions over medium heat, stirring occasionally. When the onions begin to get a little bit of golden brown color (after about 30-45 minutes), add the butter.
Step 2
Continue to cook over medium heat, stirring occasionally until the onions are deeply caramelized (the color of an old penny). This should take about an hour total. If needed, add a couple tablespoons of water to dissolve any browned bits off the bottom to prevent them from burning while the onions continue to cook.
Step 3
Once the onions are deep brown and jammy in texture, add the flour. Stir and cook the flour with the caramelized onions for about two minutes more. The flour helps thicken the broth slightly, giving it body.
Step 4
Add the beef broth to the pot and stir to dissolve any browned bits off the bottom of the pot. Also add the thyme, bay leaf, pepper, and Worcestershire sauce. Bring the soup up to a simmer, then allow it to simmer for about a half hour. If using a low sodium broth, make sure to taste the soup after simmering and add salt to taste.
Step 5
Toward the end of the simmer time, preheat the oven's broiler. Place the bread slices on a baking sheet and place them in the oven on the middle rack. Broil for a few minutes on each side, or just until they are barely golden brown (they will broil more later).
Step 6
If you do not have oven safe bowls, top each slice of bread with shredded cheese, then return them to the oven and continue to broil until the cheese is melted and bubbly. Broiling time will vary with each oven, so make sure to watch them closely. This should only take a few minutes. Place one piece of toasted bread with melted cheese on top of each bowl of soup just before serving.
Step 7
If you do have oven safe bowls, portion your soup into the bowls, top each one with a piece of lightly toasted bread, then some of the shredded cheese. Place the bowls back on the baking sheet and place everything back in the oven under the broiler. Broil for just a few minutes or until the cheese is melted and bubbly. Serve hot!