Preheat your oven to 400 degrees f.
Melt the butter in a large oven-safe skillet over medium heat.
Add the sliced onions and saute, stirring frequently for 5 minutes. Stir in 1/2 cup of broth and allow it to cook down with the onions until the liquid is nearly gone and the onions are golden-brown around 15 minutes.
Whisk together the oregano, garlic powder, Arrowroot, sea salt, and pepper. Rub each chicken breast really well with this mixture.
Once the onion is caramelized, stir in the Worcestershire sauce, then using a spatula, set this onion mixture aside on a plate.
Heat the oil in the same skillet and sear the chicken for 3-5 minutes per side until nicely golden-brown.
Pour in the remaining cup of broth and bring the sauce to a simmer. Allow it to cook with the chicken for about 10 minutes, or until the internal temperature of each chicken breast reads 165F.
Once the chicken is cooked through, top each with your caramelized onions and then top evenly with your grated cheese.
Place your skillet into your preheated oven.
Bake until the cheese is melted and bubbly, around 8-10 minutes.
Garnish with fresh herbs of choice.
Enjoy while hot!