Preheat oven to 400 degrees Fahrenheit.
Melt 1 tbsp of olive oil and 1 tbsp of butter in a frying pan over medium-low heat. Sauté onions for 2-3 minutes.
Place a few tablespoons of flour in a shallow dish and dredge each chicken breast in the flour so that each side has a light coating. Add the chicken breasts to the pan and sprinkle the Italian seasoning, salt and garlic powder evenly across all sides of the chicken breasts. Let it brown with the onions for 3-4 minutes per side. You may need to brown the chicken in batches depending on the size of your pan. Remove the chicken pieces and place them in your baking dish.
Add 1 tsp of butter to the pan with the onions. Add the sun-dried tomatoes and sauté for 2 minutes.
Add the white wine and deglaze, scraping the brown bits from the bottom of the pan.
Add the chicken broth, cream, Parmesan cheese and basil. Stir and let simmer for 2-3 minutes.
Pour the sauce over the chicken breasts in the baking dish. Bake for 15-20 minutes, or until the sauce has reduced slightly and is bubbling, and the top has browned a little.
Top with more fresh basil or parsley and fresh Parmesan or Romano cheese, if desired. Serve over pasta or a slice of crusty bread to soak up the sauce. Enjoy!