Prep the chicken: Pat the chicken dry and slice into cutlets or bite-size pieces. Season all over with salt, pepper, and a pinch of Italian seasoning.
Heat the pan: In a large skillet, warm 1 tablespoon butter and the olive oil over medium-high heat until shimmering.
Sear the chicken: Add chicken in a single layer.
Cook 3–4 minutes per side (or until just cooked through). Remove to a plate and tent loosely with foil.
Cook the veggies: In the same pan, add 1 tablespoon butter. Add broccoli and/or cauliflower with a pinch of salt.
Sauté 3–4 minutes until crisp-tender. If using zucchini ribbons, add them in the last minute so they don’t get soggy. Transfer veggies to the plate with chicken.
Build the sauce base: Reduce heat to medium-low.
Add the remaining 1 tablespoon butter and the garlic. Sauté 30 seconds, just until fragrant—don’t brown it.
Deglaze: Pour in the chicken broth and scrape up any browned bits. Let it simmer 1–2 minutes to reduce slightly.
Add the cream: Stir in heavy cream.
If using cream cheese, whisk it in now until smooth. Keep heat low and let it gently bubble for 3–5 minutes, stirring often.
Finish with Parmesan: Turn heat to low. Gradually whisk in Parmesan in small handfuls until melted and silky.
Season with salt, pepper, and a pinch of red pepper flakes if you like a kick.
Combine: Return the chicken and veggies (plus any juices) to the pan. Toss to coat and warm through 1–2 minutes. If the sauce is too thick, loosen with a splash of broth or cream.
Taste and brighten: Add a squeeze of lemon for balance (optional).
Adjust salt and pepper.
Serve: Garnish with chopped parsley or basil and extra Parmesan. Serve hot.