Cut extra fat off of chicken breasts and season with salt, pepper, thyme and paprika.
Over medium heat, warm 2 tbsp of the avocado oil and brown chicken on each side, aprx 10 minutes total. Set chicken aside.
Reduce heat to low, and add remaining 3 tbsp avocado oil to pan. Add onion rings, and toss with sugar. Cover and simmer for 15 minutes.
Remove lid and cook an additional 5 minutes to ensure onions are soft and caramelized. Next, add butter, garlic, remaining salt, pepper, and continue to heat for another 2 minutes.
Stir in the vinegar and increase heat to medium-high to bring pan to a boil. Cook until liquid is reduced by half, less than 5 minutes.
Preheat oven to 375 degrees.
Add bone broth to pan and cook another 10 minutes.
Transfer onions and liquid to a deep oven-safe casserole dish.
Slice the chicken breasts and place atop onions.
Place casserole into oven and bake for 15 to 25 minutes, or until chicken is cooked through.
Sprinkle cheese on top and put back in oven for another 5 minutes, or until cheese has melted.
Serve as a soup, garnish with parsley if you like.