Heat the olive oil in a large skillet over medium-high heat. Season the chicken breasts with salt and pepper, then add them to the skillet. Cook for about 6-7 minutes on each side, or until the chicken is cooked through and golden brown. Remove the chicken from the skillet and set aside.
In the same skillet, add the minced garlic and cook for about 30 seconds until fragrant. Be careful not to burn it.
Pour in the chicken broth and scrape the bottom of the skillet to release any browned bits. Allow it to simmer for about 2 minutes.
Reduce the heat to medium and add the heavy cream, Italian seasoning, and red pepper flakes. Stir well to combine.
Gradually add the grated Parmesan cheese, mixing until the sauce is smooth and creamy. If the sauce is too thick, you can add a bit more chicken broth to reach your desired consistency.
Add the cherry tomatoes, sun-dried tomatoes, and fresh spinach to the skillet. Stir gently until the spinach wilts and the tomatoes are heated through.
Return the cooked chicken to the skillet, spooning the sauce over the top. Allow everything to heat together for another 2-3 minutes.
Serve immediately, garnished with additional Parmesan cheese if desired.