Pat chicken breasts dry with paper towel, then season with salt and pepper and set aside.
Heat avocado oil in large frying pan over medium-high heat. When oil starts to smoke, add chicken to pan without overcrowding (you may need to sear in batches).
Sear for 3 minutes per side, until golden brown and internal temperature reaches 155 degrees Fahrenheit. Remove chicken from pan, place on a plate, and cover tightly with aluminum foil. The chicken will continue to cook to a safe eating temperature while resting.
Reduce heat to medium and add shallot to pan, moving consistently for 3 minutes until softened. Then add minced garlic and cook for an additional minute, until fragrant.
Deglaze pan with wine, being sure to scrape up fond on bottom of pan. Add anchovy paste and mix well.
Add chicken stock and butter to pan and allow to simmer until reduced by half and thickened, about 7 minutes.
Turn off heat and add lemon juice, chicken juices collected on plate, and parsley and mix well. Chef’s Note: Taste pan sauce before adding salt and pepper to taste.
Add desired amount of pan sauce to a plate and top with chicken breast.