Pat the chicken breasts dry with a paper towel. Season both sides generously with salt and pepper, then lightly dredge them in flour. This step ensures a golden sear and locks in moisture.
Heat olive oil and 1 tablespoon of butter in a large skillet over medium-high heat. Once the butter has melted and the pan is hot, add your chicken. Cook for 5-6 minutes per side until both sides are golden brown. Don’t overcrowd the pan, or you’ll lose that crispy sear. Once cooked, transfer the chicken to a plate and set aside.
Reduce the heat to medium and add the remaining butter to the skillet. Once melted, sauté the minced garlic for about 30 seconds, just until fragrant (don’t burn it!). Stir in the chicken stock, Dijon mustard, lemon zest, and juice. Mix well and scrape up browned bits from the bottom of the pan—that's where the magic is.
Return the cooked chicken breasts to the skillet, along with any juices they released while resting. Spoon the sauce over the chicken. Cover the skillet with a lid and simmer for 5-7 minutes until the chicken is cooked fully and reaches an internal temp of 165°F.
Turn off the heat, sprinkle fresh parsley over the chicken, and get ready for compliments! Serve immediately while the sauce is still warm and creamy.