Toss the butter, oil, onions and water into a large soup pot with a few pinches of salt.
Cover with a tight fitting lid and let the onions soften over a medium high heat, about 10 minutes.
When the water has evaporated, remove the lid, turn heat to low and begin to slowly caramelize onions, stirring frequently. This will take about one hour.
When the onions are a deep golden colour and have shrunk dramatically, add the brandy, thyme and broth.
Season with salt and pepper and let simmer for 15 minutes.
Preheat your oven's broiler. Ladle the soup into 4 onion soup or ovenproof bowls and fit a slice of toast over each bowl.
Sprinkle each evenly with the cheese and place bowls onto a baking sheet.
Place under the broiler and broil until the soup is bubbling and the tops are golden brown.