Slice the chicken breasts horizontally to create thinner cutlets.
In a small bowl, combine the garlic powder, paprika, oregano, salt, and black pepper. Season both sides of the chicken evenly.
Heat the avocado oil in a large skillet over medium-high heat. Add the chicken and cook for about 4–5 minutes per side, or until cooked through. Transfer the chicken to a clean plate.
Reduce the heat to low-medium. Add the butter and onions to the same skillet. Cook for 10–15 minutes, stirring occasionally, until the onions become soft and beautifully golden.
Add the balsamic vinegar and honey. Cook for another 1–2 minutes, stirring to coat the onions.
Increase the heat and whisk in the chicken broth. Bring the mixture to a boil, scraping up any flavorful browned bits from the skillet.
Reduce the heat to low and pour in the heavy cream. Let the sauce gently simmer for 1–2 minutes, until slightly thickened.
Stir in the Parmesan cheese, if using. If the sauce becomes too thick, add a splash of chicken broth.
Return the chicken to the skillet and spoon the creamy onion sauce over the top. Simmer gently for another minute or two to warm everything through.
Serve the Creamy Caramelized Onion Chicken with rice, pasta, mashed potatoes, or steamed vegetables.