Heat a large skillet over medium-high heat. While the pan is heating up, generously season your chicken breasts on both sides with salt and freshly cracked black pepper.
Once the pan is hot, add the olive oil and the chicken breasts. Sear on each side for 3-4 minutes (if your chicken is really thin, aim for about 2 minutes). It'll finish cooking later. Remove the seared chicken breasts from the pan, set them aside on a plate, and reduce the heat to medium.
Add two tablespoons of the broth, scraping up any of the browned bits stuck on the bottom of the pan and add in the minced garlic. Cook, stirring frequently for about 30 seconds before adding in the Italian seasoning (or thyme), mustard, and butter. Stir together and continue to cook until melted before adding in the rest of the broth, the lemon juice, lemon zest, and sugar. Give the sauce a quick stir and add the chicken back in the pan.
Cover with a lid and reduce heat to medium-low. Cook for 5 more minutes, or until the chicken reaches an internal temperature of 165ºF. Serve with freshly chopped parsley and thin slices of lemon or freshly grated lemon zest.