Begin by lining a baking sheet with foil and placing the beef ribs side by side. Position an oven rack in the top third of the oven and broil the ribs for 12-15 minutes, flipping halfway through, until they are beautifully browned.

Transfer the roasted bones and any juices to an 8-quart stock pot. Add the chopped onion, carrots, celery, bay leaves, and smashed garlic before pouring in 20 cups of water. Bring everything to a simmer, skimming off any foam that rises to the surface. Allow it to simmer until the liquid reduces by just over half, resulting in 8-10 cups of broth. Once ready, strain the broth through a mesh strainer into mason jars and discard the solids.

Use a mandoline to slice the white and yellow onions into 2 mm thick pieces and set them aside.

In a large Dutch oven, melt the butter over medium heat. Once it’s foamy, add the sliced onions, ensuring they are well-coated. Cover the pot for the first 5 minutes, then uncover, reduce the heat to medium-low, and season with salt and pepper. Stir in the sliced garlic and bay leaves, cooking until deeply golden brown, about 45 minutes to an hour.

Once caramelized, increase the heat to medium and add the Dijon mustard, Worcestershire sauce, and thyme leaves. When the onions start sizzling, introduce vermouth and simmer for an additional 5 minutes.

Pour the prepared beef stock into the caramelized onions and bring it to a gentle simmer. Allow it to simmer for 15-20 minutes until slightly thickened, adjusting seasoning with salt and pepper as needed.

Preheat the oven to 425°F. Arrange baguette slices on a baking sheet, spreading softened butter over each. Season and toast for 7-10 minutes, until golden brown. Rub each slice with a clove of garlic afterward.

Ladle the soup into oven-safe bowls. Top with toasted bread slices and generously sprinkle shredded Gruyère cheese. Bake for 10 minutes, broiling briefly if desired until the cheese is melted and bubbly.