Thinly slice the yellow onions into uniform half-moons.
In a large pot over medium heat, melt the ghee and add the onions with a pinch of sea salt.
Cook the onions for 25-30 minutes, stirring occasionally, until they are deep golden brown and caramelized.
Stir in the balsamic vinegar to deglaze the pan, scraping up any browned bits from the bottom.
Add the beef bone broth, shredded beef, dried thyme, and bay leaf to the pot.
Bring to a simmer and cook for 15 minutes to allow the flavors to meld, then remove the bay leaf.
Season with the remaining sea salt and black pepper.
Preheat your broiler and ladle the soup into an oven-safe crock.
Place the sourdough slice on top of the soup and cover with the shredded Gruyere cheese.
Broil for 2-3 minutes until the cheese is melted, bubbly, and slightly browned.