Prep the chicken. Pat the chicken breasts dry.
Season both sides with salt, pepper, Italian seasoning, and paprika. Pounding to 1/2–3/4 inch thick helps them cook evenly and stay juicy.
Heat the pan. Set a large skillet over medium-high heat. Add olive oil and the reserved teaspoon of sun-dried tomato oil for extra flavor.
Sear the chicken. Add chicken and cook 5–6 minutes per side until golden and cooked through (internal temp 165°F).
Transfer to a plate and tent loosely with foil.
Sauté aromatics. Reduce heat to medium. If the pan looks dry, add a splash more oil. Add shallot and cook 1–2 minutes until softened.
Stir in garlic for 30 seconds until fragrant.
Deglaze. Pour in chicken broth and scrape up browned bits. Let it simmer for 1–2 minutes to concentrate flavor.
Build the sauce. Stir in heavy cream and sun-dried tomatoes. Simmer gently 2–3 minutes to thicken slightly.
If using cream cheese, whisk it in now until smooth.
Add spinach and cheese. Fold in spinach until just wilted. Stir in Parmesan until melted and silky. Add lemon juice and a pinch of red pepper flakes if you like a little heat.
Finish with chicken. Return chicken and any juices to the pan.
Spoon sauce over the top and simmer 2 minutes so flavors mingle. Adjust seasoning with salt and pepper.
Garnish and serve. Sprinkle with fresh basil. Serve hot over zucchini noodles, cauliflower rice, or sautéed greens.