Pat chicken breasts dry with paper towels. Using a sharp knife, trim any visible fat. If breasts are uneven in thickness, place between two sheets of plastic wrap and gently pound to an even 3/4-inch thickness.
In a small bowl, combine olive oil, minced garlic, chopped rosemary, thyme, oregano, lemon zest, lemon juice, Mrs. Dash, and black pepper.
Place chicken in a glass dish or resealable bag. Pour 3/4 of the herb mixture over chicken, reserving the remainder. Massage mixture into chicken. Refrigerate for 30-45 minutes (not longer, as acid can toughen meat).
Remove chicken from refrigerator 15 minutes before cooking to take the chill off.
Heat a heavy-bottomed skillet over medium heat until hot but not smoking.
Place chicken breasts in skillet presentation-side down. Cook undisturbed for 5-6 minutes until golden brown.
Turn chicken over, reduce heat to medium-low. Add reserved herb mixture and chicken broth. Cover and cook for 7-9 minutes until internal temperature reaches 155°F.
Transfer chicken to a cutting board. Tent loosely with foil and rest for 5 minutes (temperature will rise to safe 165°F).
While chicken rests, increase heat to medium-high and reduce remaining liquid in pan until slightly thickened, about 3 minutes.
Slice chicken against the grain, drizzle with reduced sauce.