Prep the chicken. Pat chicken dry.
Season both sides with 1 teaspoon salt and 1/2 teaspoon black pepper. If the breasts are thick, pound to an even 1/2–3/4 inch for quicker, more even cooking.
Brown the chicken. Heat 2 tablespoons olive oil in a large skillet over medium-high. Add the chicken and sear 4–6 minutes per side until golden.
Transfer to a plate; it doesn’t need to be fully cooked yet.
Sauté the aromatics. Lower heat to medium. Add a drizzle more oil if needed. Stir in the minced garlic and sliced sun-dried tomatoes.
Cook 1–2 minutes until fragrant, being careful not to burn the garlic.
Deglaze. Pour in the white wine and scrape up browned bits. Let it reduce by about half, 2–3 minutes. If not using wine, use broth and a squeeze of lemon later to brighten.
Build the sauce. Stir in the chicken broth and bring to a gentle simmer.
Add the cream and a pinch of red pepper flakes if you like subtle heat. Simmer 2–3 minutes to thicken slightly.
Add Parmesan. Sprinkle in the Parmesan, stirring until it melts and the sauce is smooth. Taste and adjust salt and pepper.
The sauce should be savory and balanced, not overly salty.
Finish cooking the chicken. Nestle the chicken back into the skillet with any accumulated juices. Simmer on low 5–7 minutes, turning once, until the chicken is cooked through (internal temp 165°F/74°C).
Brighten and basil. Turn off the heat. Stir in the butter (optional) and a squeeze of lemon for freshness.
Fold in most of the basil, reserving some for garnish.
Serve. Spoon the sauce over the chicken and shower with remaining basil. Serve with pasta, mashed potatoes, rice, or toasted bread. A simple green salad or steamed green beans rounds it out.