Prep the chicken: Pat the chicken dry. Season both sides with 1 teaspoon salt, black pepper, and Italian seasoning.
If using large breasts, slice them horizontally into cutlets for even cooking.
Sear the chicken: Heat olive oil and 1 tablespoon butter in a large skillet over medium-high. Add the chicken and cook until golden and mostly cooked through, about 4–5 minutes per side. Transfer to a plate and tent loosely with foil.
Build the flavor base: Lower heat to medium.
Add remaining 2 tablespoons butter. Stir in garlic and sun-dried tomatoes. Cook 30–45 seconds until fragrant, being careful not to brown the garlic.
Deglaze: Pour in chicken broth and scrape up the browned bits.
Simmer 2–3 minutes to reduce slightly.
Make it creamy: Stir in heavy cream, Parmesan, Dijon, red pepper flakes, and remaining ½ teaspoon salt. Simmer gently, stirring, until the sauce thickens enough to coat a spoon, about 3–5 minutes.
Add greens: Fold in the spinach and let it wilt into the sauce, 1–2 minutes.
Finish the chicken: Return the chicken and any juices to the skillet. Spoon sauce over the pieces and simmer on low until the chicken is cooked through (internal temp 165°F) and the sauce is silky, 3–5 minutes.
Brighten and serve: Squeeze in lemon juice, taste, and adjust seasoning with more salt, pepper, or lemon.
Garnish with chopped basil or parsley. Serve hot with pasta, rice, or bread.