Thinly slice the yellow onion into uniform half-moons.
Heat the olive oil in a heavy-bottomed pot over medium-low heat and add the onions with a pinch of sea salt.
Cook the onions slowly for 20-25 minutes, stirring occasionally, until they are deeply caramelized and jammy.
Mince the garlic and add it to the pot, sautéing for 1 minute until fragrant.
Deglaze the pot with balsamic vinegar, scraping up any browned bits from the bottom.
Pour in the beef bone broth and add the fresh thyme sprig and black pepper.
Add the pre-cooked shredded chicken breast to the pot and bring the soup to a gentle simmer for 10 minutes.
Remove the thyme sprig and ladle the soup into an oven-safe crock or bowl.
Grate the Gruyere cheese over the top of the soup.
Place the bowl under a broiler for 2-3 minutes until the cheese is melted, bubbly, and slightly golden.