Place chicken breasts between layers of wax paper (you can also use saran wrap or a large ziploc bag.) Use a meat mallet, heavy skillet, or other heavy, flat object to pound it to about 1 inch thickness.
Heat 2 Tablespoons olive oil in a large skillet over medium heat. Add the chicken breasts, season with half the salt & pepper, and pan fry for about 5 minutes, until the first side begins to brown and chicken is cooked about halfway through.
Use tongs or a fork to flip each breast. Season with remaining salt & pepper and cook for an additional 7-10 minutes, OR until meat thermometer inserted at the thickest part of the breast reads 160°F. Add chicken broth or water to the pan when it's dry to prevent over-browning.
Once chicken reaches 160°, turn off the heat and (optionally) add 1 Tablespoon butter to the pan along with any drippings in the pan. Spoon the melted butter over the chicken and garnish with parsley or other herbs as desired. (The chicken will continue cooking for a bit even after being removed from the heat.)
Let rest for 5-10 minutes before slicing.