Thaw fish, if frozen. Rinse fish; pat dry with paper towels. Preheat oven to 350 degrees F. Peel film at corner of refrigerated potatoes to vent. Heat potatoes in container in microwave on 100 percent power (high) for 3 minutes. Carefully transfer to a bowl; stir in pesto, yogurt, 1/4 teaspoon of the salt, and 1/4 teaspoon of the pepper. Set aside.
In a large skillet melt butter over medium heat. Stir in flour. Whisk in chicken broth. Cook and stir until mixture comes to a boil. Stir in edamame. Cook and stir for 3 minutes. Stir in tomatoes and basil.
Divide mixture among four 16-ounce individual casseroles or au gratin dishes. Place fish on top of bean-tomato mixture. Sprinkle fish with the remaining 1/4 teaspoon salt and the remaining 1/4 teaspoon pepper. Divide the potato mixture among the casseroles, spooning into a mound on one side of the fish.
Bake, uncovered, 20 to 25 minutes or just until fish begins to flake easily when tested with a fork. Garnish with fresh basil.