Stir together flour, tarragon, salt, ginger, pepper, mustard powder, thyme, garlic powder, and oregano in a shallow bowl until well blended. Beat the egg together with the milk until smooth in a bowl. Dredge the chicken breasts in the flour mixture, shake off excess, then dip in egg, and again in flour. Set breasts aside to rest for 10 minutes.
Preheat oven to 350 degrees F (175 degrees C).
Heat the vegetable oil in a skillet over medium-high heat. Dredge the chicken breasts in flour again, and shake off excess. Brown the chicken in the hot oil until golden brown on both sides. Place onto a baking sheet, and bake in preheated oven until the chicken is no longer pink in the center, 20 to 30 minutes.