Pat chicken dry. Season both sides with salt, pepper, and garlic powder. Dust lightly with flour.
Heat olive oil and butter in a large skillet over medium-high heat until shimmering.
Sear chicken 4–5 minutes per side until golden. Transfer to a plate and keep warm.
Lower heat to medium. Add garlic and cook 30 seconds, stirring, until fragrant.
Whisk in chicken broth and Dijon. Scrape up browned bits and simmer 2 minutes.
Stir in heavy cream and Parmesan. Simmer, stirring, until slightly thickened, 3–4 minutes.
Add lemon juice, Italian seasoning, thyme, and half the parsley. Taste and adjust salt and pepper.
Return chicken and any juices to the pan. Spoon sauce over and simmer 5–7 minutes, until 165°F.
Rest 2 minutes off heat. Sprinkle with remaining parsley and serve warm.