Trim all visible fat and undesirable parts from chicken breasts, then make very small slits crosswise down the length of each breast.
Season chicken with poultry seasoning on both sides.
Heat olive oil in large frying pan big enough to hold the chicken in a single layer, add chicken and cook about 4 minutes on the first side, until chicken is lightly browned.
Turn chicken over and cook 2-3 minutes on the second side, until chicken feels almost, but not quite firm to the touch.
While chicken cooks, put all sauce ingredients in bowl or large measuring cup, and whisk to combine.
When chicken is lightly browned, lower heat and pour sauce over.
Simmer 20 minutes, being sure to keep heat at a very low simmer.
When the sauce is mostly reduced, remove chicken from pan and whisk the sauce a few times to be sure it’s smooth.
Season to taste with a little salt and fresh-ground black pepper.
Serve hot, with a little sauce spooned over each piece of chicken, garnishing with fresh parsley if desired.