Pat chicken dry with paper towels and sprinkle with 1/2 teaspoon of salt and pepper.
Add butter and 1 tablespoon oil to a large pan over medium high heat. Once shimmering, add the chicken breasts, and sear on each side until golden, and easy to flip--about 4-5 minutes. Once the chicken is almost totally seared on the second side, reduce the heat of your pan to low and place a lid on top. Continue to cook until your chicken reaches an internal temp of 165 F at the thickest part. Set aside on a plate and tent with foil.
Increase the heat of your pan to medium. Add the remaining tablespoon of oil and the garlic, and continue to saute until fragrant, about 1 minute.
Add the heavy cream, chicken broth, Italian seasoning, and parmesan cheese, and stir. Use the back of a wooden spoon to loosen any brown bits that have accumulated on the bottom of your pan, and stir to incorporate them into the sauce. Continue to cook until the cheese melts.
Add the spinach and sun dried tomatoes, and stir just until the spinach wilt. Remove from heat. Place a piece of chicken on eat place and drizzle sauce on top. Enjoy!