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 golden and cooked through to an internal temperature of 165°F (74°C). Transfer the chicken to a plate.
Reduce the heat to low-medium. Add the butter and onions to the same skillet. Cook for 10–15 minutes, stirring regularly, until the onions become soft, golden, and caramelized.
Stir in the balsamic vinegar and honey. Cook for another 1–2 minutes, allowing the flavors to blend with the onions.
Increase the heat and pour in the chicken broth. Bring it briefly to a boil while stirring and scraping up the flavorful browned bits from the bottom of the skillet.
Reduce the heat to low and pour in the heavy cream. Allow the sauce to gently simmer for 1–2 minutes, or until it begins to thicken. Add a splash of extra chicken broth if the sauce becomes thicker than desired.
Stir in the Parmesan cheese until melted and smooth. Return the chicken to the skillet and spoon the creamy sauce and onions over the top.
Serve the Creamy Caramelized Onion Chicken warm with rice, pasta, mashed potatoes, or steamed vegetables.
Notes
For a slightly lighter sauce, replace part of the heavy cream with additional chicken broth, although the finished sauce will be thinner.