Sear the Chicken: Pat the chicken breasts completely dry with paper towels. Season both sides generously with salt, black pepper, and Italian seasoning. Heat the olive oil in a large skillet over medium-high heat. Add the chicken breasts and cook for 5 to 6 minutes per side, until a golden crust develops and the internal temperature reaches 165°F (74°C). Transfer to a plate, cover loosely with foil, and set aside.

Build the Flavor Base: Lower the skillet heat to medium. Melt the butter in the same pan, using a wooden spoon to scrape up any browned, savory bits from the bottom. Add the minced garlic and sauté for 1 minute until fragrant. Stir in the halved cherry tomatoes and chopped sun-dried tomatoes. Cook for 3 to 4 minutes, stirring occasionally, until the cherry tomatoes soften and turn soft and jammy.

Create the Cream Sauce: Pour in the heavy cream and chicken broth, stirring well. Bring the mixture to a gentle simmer. Gradually stir in the freshly grated parmesan cheese until it completely melts and the sauce becomes smooth and velvety. Let simmer for 2 to 3 minutes to thicken slightly, then stir in the fresh baby spinach for about 1 minute until it gently wilts.

Combine and Serve: Return the seared chicken breasts and any accumulated plate juices back into the skillet. Spoon the rich cream sauce, jammy tomatoes, and wilted spinach over the top of the chicken. Simmer together for 2 minutes until everything is heated through. Turn off the heat and garnish with an extra dusting of parmesan cheese and coarsely cracked black pepper. Serve immediately.