Prep the chicken: Pat the chicken dry and slice into thin, even strips. Season generously with salt and pepper. If you like, add a pinch of Italian seasoning.
Blanch the broccoli: Bring a pot of salted water to a boil.
Add the florets and cook 2–3 minutes until bright green and crisp-tender. Drain and set aside. (If using frozen, thaw and pat dry.)
Sear the chicken: Heat olive oil and 1 tablespoon butter in a large skillet over medium-high. Add chicken in a single layer.
Cook 4–6 minutes, turning once, until browned and cooked through. Transfer to a plate; tent with foil.
Sauté the garlic: Lower heat to medium. Add remaining 2 tablespoons butter to the skillet.
Stir in garlic and cook 30–45 seconds until fragrant. Do not brown.
Build the sauce: Pour in chicken broth and scrape up browned bits. Stir in heavy cream.
If using cream cheese, whisk it in now until smooth.
Thicken gently: Simmer on low for 3–5 minutes, stirring often, until slightly thickened. Avoid a hard boil to prevent separation.
Add Parmesan: Remove the pan from direct heat. Sprinkle in Parmesan a handful at a time, whisking until melted and silky.
Return to low heat only if needed to fully melt.
Season: Taste and add salt, pepper, and a pinch of red pepper flakes if you like gentle heat. A small squeeze of lemon brightens the richness.
Combine: Return chicken and any juices to the skillet. Add broccoli.
Toss to coat in the sauce and warm through 1–2 minutes.
Serve: Garnish with chopped parsley and extra Parmesan. Enjoy as-is, or over zucchini noodles, spaghetti squash, or cauliflower rice for a bigger bowl.