Combine first 7 ingredients in a medium bowl, stirring with a whisk. Reserve 1 1/2 tablespoons cilantro mixture. Add farro to remaining cilantro mixture; toss to coat.
Divide farro mixture, chopped grilled vegetables, beans, cheese, and avocado among 4 shallow bowls. Drizzle with reserved 1 1/2 tablespoons cilantro mixture. Serve with lime wedges.
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