Place chicken breasts on cutting board. Hold breast flat, and cut in half lengthwise into 2 even pieces keeping sharp knife parallel to cutting board, to make 2 cutlets. Repeat with other chicken breast.
Pat each chicken cutlet dry with paper towel. Generously season each side with salt and black pepper. Add all-purpose flour to shallow bowl, with tongs, dunk each chicken cutlet in flour until fully coated on each side, then place on large plate.
Warm olive oil in large skillet over medium high heat. Once hot, swirl skillet to cot evenly with oil, then add each chicken cutlet, and cook for 4 to 5 minutes on each side (flipping only once), until chicken is cooked and browned. Then remove chicken and place on plate, loosely cover with foil to keep warm, and set aside.
Add chopped shallots, chopped leeks, sliced mushrooms, and minced garlic to skillet, and cook until softened, about 5 to 6 minutes, stirring often.
Then add white wine, scrape any bits left in skillet with wooden spoon and continue cooking for about 5 to 6 minutes, until it has reduced just a little, stirring occasionally.
Add fresh thyme, heavy cream and Dijon mustard, stir it in until fully incorporated, and cook for another 5 to 6 minutes, stirring a few times.
Add a pinch of salt, black pepper to taste, and fresh chopped parsley. Transfer chicken cutlets back into skillet, and cook until warmed through about 3 minutes, or until chicken has reached internal temperature of 165° when checked with meat thermometer. Serve warm with rice, or side of choice.