Pat the chicken breasts dry with paper towels. If they are very thick, slice them in half horizontally or gently pound them to an even thickness so they cook evenly and stay tender.
Season both sides of the chicken with salt, black pepper, and Italian seasoning, rubbing the seasoning over the chicken so each piece is well covered.
Heat a large skillet over medium-high heat and add the olive oil. Once hot, add the chicken and cook for about 4–5 minutes per side, depending on thickness, until golden brown and the center reaches 165°F (74°C). Transfer the chicken to a clean plate.
Reduce the skillet heat to medium and add the butter. Once melted, add the minced garlic and cook for about 30 seconds, stirring constantly, until fragrant but not browned.
Pour in the chicken broth and heavy cream. Stir well and scrape the browned bits from the bottom of the skillet. Let the sauce gently simmer for about 3–4 minutes so it begins to thicken.
Lower the heat and stir in the grated Parmesan cheese. Keep stirring until the cheese melts into the sauce and the mixture becomes creamy. Do not let the sauce boil hard after adding the Parmesan.
Add the fresh spinach to the skillet and gently stir it into the sauce. Cook for about 1–2 minutes, until the spinach wilts down and becomes tender.
Place the cooked chicken back into the skillet and spoon the creamy spinach sauce over the top. Let everything simmer gently for another 1–2 minutes so the chicken warms through and absorbs some of the sauce.
Taste the sauce and add a little more salt or pepper if needed. Be careful with the salt because Parmesan already adds salty flavor.
Sprinkle fresh parsley over the chicken and spoon plenty of the creamy Florentine sauce over each piece. Serve while the sauce is warm and creamy.