Melt the butter and olive oil together in a large, heavy-bottomed pot over medium heat. Add the sliced onions and a pinch of salt. Cook low and slow, stirring frequently for about 40 to 50 minutes, until the onions are deeply browned, soft, and sweet.
Stir in the minced garlic and thyme during the last 5 minutes of cooking.
Sprinkle the plain flour over the caramelised onions and cook for 1 to 2 minutes, stirring constantly to get rid of the raw flour taste.
Pour in the dry white wine to deglaze the pot, scraping up any delicious browned bits stuck to the bottom. Let it simmer until the wine has mostly reduced.
Gradually whisk in the beef stock along with the Worcestershire sauce.
Bring the soup to a gentle simmer, reduce the heat, and let it bubble uncovered for about 20 to 30 minutes so the flavours meld beautifully. Season with salt and pepper to taste.
Slice the baguette and toast the rounds lightly. Spread a thin layer of wholegrain mustard onto each toast, then generously top them with the grated Sussex Charmer or mature cheddar.
Ladle the hot soup into oven-safe bowls. Float the cheesy toasts on top of the soup.
Place the bowls under the grill for 3 to 5 minutes until the cheese is bubbling, golden brown, and slightly crisp at the edges. Serve immediately!