Line 2 baking trays with aluminum foil; set aside.
Stir together flour, salt, pepper, tarragon, ginger, mustard powder, thyme, garlic powder, and oregano in a shallow bowl until well-blended. Beat together egg and milk in a separate bowl until smooth.
Dredge chicken breasts in flour mixture, shake off excess, then dip in egg, and again in flour. Place coated chicken breasts on one of the prepared baking trays; set aside to rest for 10 minutes.
Preheat the oven to 350 degrees F (175 degrees C).
Dredge chicken breasts in flour once more; shake off excess.
Heat vegetable oil in a skillet over medium-high heat. Cook chicken breasts in hot oil until golden brown, 2 to 3 minutes per side. Place fried chicken breasts on the second prepared baking tray.
Bake in the preheated oven until no longer pink in the center and the juices run clear, about 20 to 30 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).