Coarsely slice enough cabbage to make 5 cups, discarding any tough ribs (reserve remaining cabbage for salad another day).
Cut Chicken into bite-sized pieces.
In 12-inch skillet over medium heat, in 2 tablespoons hot salad oil, cook sliced cabbage and 1 teaspoon salt, stirring frequently, until lightly browned and tender, about 3 minutes. With slotted spoon, remove chicken to bowl with cabbage.
Into drippings remaining in skillet, stir mayonnaise and milk until smooth; over low heat, heat through, stirring constantly. Pour mayonnaise mixture over chicken mixture in bowl. Add zucchini, carrot, and basil; gently toss to mix well.
Serves 4-6
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