Step 1: Prepare the chicken. Pat the chicken breasts dry with paper towels. Season both sides generously with salt and pepper.
Step 2: Sear the chicken. Heat olive oil in a large skillet or oven-safe pan over medium-high heat. Add the chicken breasts and sear for 4-6 minutes per side, until golden brown and cooked through (internal temperature of 165°F / 74°C). Remove chicken from the skillet and set aside on a plate, tented with foil to keep warm.
Step 3: Sauté aromatics. Reduce heat to medium. Add butter to the same skillet. Once melted, add the diced onion and cook for 3-5 minutes until softened and translucent. Add the minced garlic and cook for another minute until fragrant, being careful not to burn it.
Step 4: Build the cream sauce. Pour in the chicken broth and deglaze the pan, scraping up any browned bits from the bottom. Stir in the heavy cream, Italian seasoning, and a pinch of nutmeg (if using). Bring the sauce to a gentle simmer.
Step 5: Wilt the spinach. Add the fresh spinach to the simmering cream sauce in batches, if necessary. Cook, stirring frequently, until the spinach has wilted completely, about 2-3 minutes.
Step 6: Finish the sauce. Stir in the grated Parmesan cheese until melted and the sauce is smooth and slightly thickened. Taste and adjust seasoning with salt and pepper as needed.
Step 7: Combine and serve. Return the cooked chicken breasts to the skillet, spooning the creamy spinach sauce over them. Garnish with extra Parmesan cheese if desired. Serve immediately with your favorite sides.