Beat the egg together with the milk in a shallow bowl. Combine the walnuts, flour, tarragon, and salt in a second shallow bowl. Dip the chicken strips first into the egg mixture, then into the flour mixture, coating evenly, and place on a plate.
Melt the butter with the oil in a large skillet over medium-high heat. Fry the chicken in small batches in the butter mixture until the coating is browned and crispy, about 5 minutes. Test one to be sure it is cooked through. Chicken should be no longer pink and juices run clear. Drain on paper towels.
