Season both sides of the chicken breast with thyme, salt and pepper.
Heat the avocado oil in a large skillet over medium high heat.
Brown the chicken breast on both sides and cook until an internal thermometer reads 165F.
Remove from the skillet and set aside.
Reduce heat to medium and add the butter, onions and ½ cup beef broth to the skillet.
Cook the onions until browned and caramelized. Add more beef broth if the onions start to dry out.
The caramelized onions will take about 20 minutes.
Add in the mushrooms to the caramelized onions and cook for 5 minutes more.
Stir in any remaining beef broth.
Add the chicken breast back to the skillet and use a spoon or tongs to smother them with the onion and mushroom mixture.
Top each chicken breast with a slice of swiss cheese.
Cover with a lid to melt.