Slice each chicken breast horizontally to create thinner pieces of relatively even thickness.
Combine the garlic powder, paprika, oregano, salt, and black pepper in a small bowl. Season the chicken evenly on both sides.
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. Transfer the chicken to a plate and set aside.
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, 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, stirring and scraping up the flavorful browned bits from the bottom of the skillet. Bring to a brief boil.
Reduce the heat to low and add the heavy cream. Gently simmer for 1–2 minutes, or until the sauce begins to thicken. Add a splash more chicken broth if necessary.
Stir in the Parmesan until melted and smooth. Return the chicken to the skillet and spoon the creamy sauce and onions over each piece.
Allow the Creamy Caramelized Onion Chicken to warm in the sauce briefly before serving.
Notes
Yellow or sweet onions work particularly well for this caramelized onion chicken recipe. Shallots can also replace part of the onion for a slightly more delicate flavor.