In saucepan cook onion in 2 teaspoons of hot oil over medium heat 5 minutes or until tender, stirring occasionally. Add carrots and garlic; cook and stir 1 minute more. Add broth and edamame. Bring to boiling; reduce heat. Simmer, uncovered, for 5 minutes or until edamame and carrots are tender. Stir in thyme.
Meanwhile, in a small bowl beat egg white and water with a fork until frothy. Place bread crumbs in another small bowl. Dip feta cubes, one at a time, into egg white to coat. Allow excess egg white mixture to drip off; coat feta cubes with bread crumbs. In large skillet, heat remaining 2 teaspoons oil over medium-high heat. Add feta cubes. Cook 2 to 3 minutes or until browned but not softened, turning carefully to brown all sides of cubes. Drain on paper towels.
Ladle soup into bowls. Top with feta croutons and, if desired, additional thyme. Makes 6 (3/4 cup) side-dish servings.