Toast the bread: Preheat oven to 475°F. Arrange the bread slices on a baking sheet and toast lightly, about 4 to 5 minutes. Set aside.
Soften the onions: Melt the butter in a medium ovenproof skillet over medium-high heat. Add the onions and season with salt and pepper. Cover with a lid and cook, stirring occasionally, until softened, about 3 to 5 minutes.
Caramelize: Remove the lid, stir in the thyme and garlic, and continue cooking and stirring until the onions are deep golden brown, about 15 minutes. As they cook, add a tablespoon of water and stir. Once it evaporates, repeat with additional tablespoons of water. This keeps the onions from burning and speeds up caramelization.
Add the vinegar: Stir in the balsamic vinegar and Worcestershire sauce and cook for 1 more minute.
Add chicken and broth: Stir in the chicken and broth, scraping up any browned bits from the bottom of the pan. Taste and season with salt and pepper. Bring to a boil, then remove from the heat.
Top it: Arrange the toasted bread slices over the chicken and onion mixture in a single layer, then sprinkle the cheese over the top.
Bake: Place the skillet in the 475°F oven for 5-10 minutes, until the cheese melts and starts to brown.
Serve: Garnish with chopped fresh parsley or thyme, if desired, and serve right away.