To prevent the flounder from flaking apart before serving, use a long, flat spatula to gently remove each fillet from the broth.
Heat a large saucepan over medium-high heat. Add oil; swirl. Add mushrooms; sauté 2 minutes. Add stock and next 6 ingredients (through ginger); bring to a boil. Reduce heat; simmer 5 minutes.
Add fish to pan. Top with bok choy and edamame. Cover; simmer 6 to 8 minutes or until fish is done.
Remove fish from pan; divide evenly among 4 bowls. Divide stock mixture among bowls. Top evenly with green onions, bell pepper, and sesame seeds.
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