In 10-inch nonstick skillet, heat oil over medium heat. Add onion; cook about 5 minutes, stirring occasionally, until translucent. Add garlic; cook, stirring frequently, until softened.
Spray 3- to 4-quart slow cooker with cooking spray. In cooker, mix sweet potatoes, barley, thyme, salt and 3 cups of the broth. Add onion-garlic mixture.
Cover; cook on Low heat setting 4 to 5 hours.
In 2-cup microwavable measuring cup, microwave remaining 1 cup broth on High 2 to 3 minutes or until boiling. Stir thawed edamame and boiling broth into barley mixture in cooker. Increase heat setting to High; cover and cook 25 to 30 minutes longer or until edamame are tender. Serve in shallow bowls; sprinkle with cheese.