Season chicken breasts with Italian seasoning, salt, and pepper. Pound to even thickness if needed.
Heat olive oil and 1 tablespoon butter in a large oven-safe skillet over medium-high heat. Sear chicken 5-6 minutes per side until golden and cooked through. Remove and set aside.
Reduce heat to medium. Add remaining butter and saute garlic for 30 seconds until fragrant.
Pour in chicken broth, scraping up browned bits. Add heavy cream and bring to a gentle simmer.
Stir in Parmesan cheese until melted and sauce is smooth and slightly thickened, about 3-4 minutes.
Add spinach in batches, stirring until wilted. Season with red pepper flakes if using.
Nestle chicken back into the sauce. Spoon sauce over the chicken and serve with crusty bread or pasta.