Microwave the cream cheese in a microwave-safe bowl until very soft, about 20–30 seconds; cut into smaller pieces and set aside.
Slice each chicken breast in half lengthwise to make four thin cutlets, then season both sides with garlic powder, salt, and pepper.
Heat the butter and olive oil together in a large skillet over medium-high heat until shimmering.
Add the chicken to the hot skillet and cook 5–6 minutes per side, until golden and an instant-read thermometer reads 165°F (74°C). Transfer cooked chicken to a plate.
Reduce heat to medium and add the chopped onion to the skillet; sauté 5–7 minutes until softened and lightly browned.
Stir in the minced garlic and cook about 30 seconds until fragrant.
Pour in the chicken broth, then add the softened cream cheese, Italian seasoning, and crushed red pepper flakes; stir continuously until the cream cheese melts and the sauce becomes smooth, about 2–3 minutes. Add a splash more broth if needed to reach desired consistency.
Return the chicken to the skillet and warm through in the sauce for 1–2 minutes. Taste and adjust salt and pepper as needed, then sprinkle with chopped parsley if using and serve immediately.