Pat chicken breasts dry, and if necessary, cut in half horizontally.* Place each breast or cutlet on a cutting board and pound with a mallet until about ¼ inch thick. Season with salt and pepper on both sides.
In a large skillet on medium high heat, heat oil until shimmering. Cooking in batches, add the chicken in one layer, adding oil as needed. Brown for 3-4 minutes on each side, until cooked through. Remove chicken from the pan and set aside.
In the same skillet on medium heat, add butter, garlic, and Italian seasoning. Whisk together and sauté for 1 minute. Add flour and cook for 30 seconds. Add broth, heavy cream, and parmesan and whisk to combine. Heat until bubbling and simmer 3-5 minutes until slightly thickened. Add chicken along with any juices and sundried tomatoes and simmer for 2-3 minutes or until chicken is heated through.
Garnish with basil and parmesan cheese if desired. Season with salt and pepper and serve immediately over pasta, rice, or potatoes.
Notes
*For very thick breasts, pat dry and place flat on a cutting board.
With knife parallel to the board, cut each breast in half horizontally through the middle to make 2 slices, each slice being half as thick.
Use a paper towel and the flat of your hand to hold the breast in place as you cut.
Place each slice between 2 layers of plastic wrap.
Pound with a mallet until ¼ inch thick.
Keep leftovers in an airtight container in the refrigerator for 4 days.