Do ahead: Cook barley according to package instructions until tender. Drain cooked barley in colander. Rinse, tossing, with cold water until starchiness is washed off.
In a large mixing bowl, combine all remaining ingredients. Stir to combine well. Add rinsed/drained cooked barley. Stir to combine.
Add additional kosher salt and pepper as needed. Let salad chill 1-2 hours, covered, for flavors to meld before serving.
Notes
Prep Ahead: Mix the dressing in advance; whisk together the lime juice, olive oil, and seasonings and keep it refrigerated until you're ready to use it. Just be sure to give it a good stir before using.
Storage: Store leftover barley salad in an airtight container in the refrigerator for up to 4 days. Stir again before serving, and add a squeeze of fresh lime juice if needed to brighten the flavor.
Cook Time: The total time listed here includes chill time. The actual cook time will vary, depending on whether you use hulled or pearl barley. Follow package instructions for cook time.