Prep the chicken: Pat chicken dry and season both sides with salt and pepper.
If using breasts, slice them in half horizontally for even cooking.
Heat the pan: Set a large skillet over medium-high heat. Add oil and half the butter. When the butter foams, add the chicken in a single layer.
Sear the chicken: Cook without moving 4–5 minutes per side (thighs may need a bit longer) until golden and cooked through.
Transfer to a plate and tent with foil.
Sauté the garlic: Reduce heat to medium. Add remaining butter to the skillet. Stir in the minced garlic and cook 30–60 seconds until fragrant, not browned.
Deglaze: Pour in the chicken broth.
Scrape up browned bits from the pan with a wooden spoon. Let it simmer 2–3 minutes to reduce slightly.
Make it creamy: Stir in heavy cream, Italian seasoning, and a pinch of red pepper flakes if using. Simmer gently for 3–5 minutes until the sauce starts to thicken.
Keep heat moderate to avoid curdling.
Add Parmesan: Lower the heat and whisk in Parmesan a little at a time until melted and smooth. If the sauce is too thick, add a splash of broth; if too thin, simmer a minute longer.
Finish and season: Add lemon juice to brighten. Taste and adjust salt and pepper.
Return the chicken and any juices to the pan, stirring to coat. Warm through for 1–2 minutes.
Garnish and serve: Sprinkle with chopped parsley. Serve over sautéed spinach, roasted broccoli, zucchini noodles, or cauliflower mash.