Prep the chicken. If using thick breasts, slice them horizontally to make cutlets.
Pat dry. Season both sides with salt and pepper. Lightly dredge in flour, shaking off the excess.
Brown the chicken. Heat olive oil and butter in a large skillet over medium-high heat.
When hot and foamy, add the chicken in a single layer. Sear 3–4 minutes per side until golden. Transfer to a plate.
The chicken will finish cooking in the sauce.
Sauté aromatics. Lower heat to medium. Add garlic and sun-dried tomatoes. Cook 1 minute, stirring so the garlic doesn’t burn.
Scrape up any browned bits from the pan.
Deglaze. Pour in the chicken broth. Simmer 2–3 minutes to reduce slightly. This concentrates flavor and lifts more fond from the pan.
Make it creamy. Stir in the heavy cream, Parmesan, Italian seasoning, and a pinch of red pepper flakes if using.
Simmer gently 2–3 minutes, stirring often, until the sauce thickens enough to coat a spoon.
Add the greens. Stir in spinach and let it wilt, about 1 minute. Taste and season with salt and pepper as needed.
Finish the chicken. Return the chicken and any juices to the skillet. Nestle the pieces into the sauce.
Simmer 3–5 minutes, flipping once, until the chicken is cooked through and the sauce is glossy. Add a squeeze of lemon to brighten.
Serve. Garnish with chopped basil or parsley. Serve hot over pasta, mashed potatoes, polenta, or with crusty bread to soak up the sauce.