Pound the chicken breasts to even thickness and season both sides with salt and pepper.
Heat the olive oil in a large skillet over medium-high heat. Sear the chicken until golden and cooked through, about 3–4 minutes per side depending on thickness. Remove and set aside.
In the same skillet, add a touch more oil if needed and sauté the garlic for about 30 seconds until fragrant.
Add the spinach in batches, letting it wilt down before adding more. Stir and cook until all the spinach is wilted and reduced.
Pour in the heavy cream and chicken broth. Bring to a gentle simmer, scraping up any browned bits from the bottom of the pan.
Stir in the Parmesan cheese until melted and the sauce thickens slightly. If you like a thinner sauce, add a splash more broth.
Return the chicken to the pan and coat with the sauce. Simmer for 2–3 minutes to rewarm and meld the flavors.
Finish with lemon juice, butter if using, and a pinch of red pepper flakes for a subtle heat. Taste and adjust seasoning with salt and pepper.