1. Bring a large pot of salted water to a boil. Add the barley and boil until tender but slightly chewy, 45 minutes to 1 hour; drain.
2. In a bowl, whisk together the lime juice, honey, garlic, salt, black pepper and chili powder. Whisk in the oil; reserve 1/3 of the dressing for the barley.
3. Brush the ears of corn with dressing. Toss the bell peppers and mushrooms with remaining dressing.
4. Preheat a grill to medium-high. Season the vegetables lightly with salt; grill, turning occasionally, until tender and lightly charred, 5 to 7 minutes a side.
5. Toss barley with 1 tablespoon of the basil and the reserved dressing. Spoon onto serving plates and top with vegetables. Sprinkle with remaining basil and the feta.