Cook barley according to package directions; drain. Transfer to a large serving bowl; cool to room temperature.
In a microwave-safe dish, combine broccoli and the water. Microwave on 100% power (high) 2 to 3 minutes or just until broccoli turns bright green and is slightly tender, stirring once. Drain well. Stir into cooked barley.
For dressing, in a screw-top jar, combine vinegar, oil, Italian seasoning, mustard and salt. Cover and shake well. Toss avocado with the lime juice. Add dressing, avocado and nuts to the barley-broccoli mixture; gently toss to combine. Serve at room temperature. Sprinkle with feta cheese. Store in the refrigerator.
Tip: If you prefer, substitute farro, quinoa or brown rice for the barley. Start with the dry amount that yields 1½ cups cooked.