Season the chicken generously with salt and pepper. If you have time, let it rest seasoned for 10 minutes to boost flavor.
Heat the olive oil in a large skillet over medium-high heat. Sear the chicken on both sides until golden and almost cooked through, about 3–4 minutes per side depending on thickness. Transfer to a plate and tent with foil to keep warm.
In the same skillet, add butter and a touch more oil if needed. Sauté the minced garlic for about 30 seconds until fragrant, then pour in the broth to deglaze, scraping up any browned bits from the bottom.
Stir in the heavy cream and bring to a gentle simmer. Add parmesan cheese and whisk until melted and smooth. If you prefer a lighter sauce, you can reduce the amount of cream slightly.
Add the spinach in handfuls, allowing each batch to wilt before adding more. Cook until the spinach is fully wilted and the sauce has thickened to a creamy consistency.
Return the chicken to the pan, spooning the sauce over the pieces. Simmer for 2–3 minutes to reheat the chicken and finish cooking through. If using lemon juice, stir it in now for brightness.
Taste and adjust seasoning with salt, pepper, and red pepper flakes if using. Serve immediately, spooning extra sauce over each piece of chicken.