Heat the ghee in a medium pot over medium-low heat.
Add the thinly sliced onions and cook slowly for 20-25 minutes, stirring occasionally, until they are deep golden brown and caramelized.
Stir in the dried thyme, sea salt, black pepper, and coconut aminos, cooking for another 2 minutes.
Pour in the beef bone broth and bring the mixture to a gentle simmer for 10 minutes to allow the flavors to meld.
Add the shredded chicken breast to the pot and stir until the protein is heated through.
While the soup simmers, lightly toast the sourdough bread slice.
Ladle the soup into an oven-safe bowl, place the toasted sourdough on top, and sprinkle evenly with the shredded Gruyere cheese.
Place the bowl under a broiler for 2-3 minutes until the cheese is bubbly and slightly browned.
Garnish with fresh parsley and serve immediately.