Gather all ingredients and equipment.
Preheat the oven to 350°F (180°C).
In a small bowl, mix together the miso, the whites of the green onions, 1 tsp of sesame oil, ginger, honey, and 1 tsp soy sauce. Set aside.
Coat the fish filets on both sides with miso mixture and set aside.
Place the bok choy, edamame, and mushrooms in a medium bowl. Add 1 tsp of soy sauce, 1 tsp sesame oil, and half of the ginger and toss gently to coat.
Fold 2 pieces of parchment paper or foil until they are almost a 15 inch x 12 inch square.
Starting at one end of the folded edge, cut a half of a heart shape in such a way that when the parchment is opened it is in the shape of a heart with the folding crease down the center.
To assemble the pouches, divide the bok choy, edamame and mushrooms mixture between the two hearts, placing the mixture on one half of each heart.
Top the vegetables with one 4-ounce filet of fish.
Top each filet with lime juice.
To close the pouches, fold the top of the heart over the fish and vegetables.
Then starting at the top curve of the heart, make a fold, overlapping your folds to create a sealed crimped outer edge. Continue working around the base of the heart until you get to the bottom point. Twist tightly and fold into a crimp to completely seal your packet.
Arrange the packaged fish on a baking tray and place in the oven.
Cook until the fish is fully cooked through (white and flaky) and has an internal temperature of 140F, about 12-15 minutes.
Place each pouch on a plate and let stand about 30 seconds to cool before opening to avoid burns.
There will be some hot steam that escapes when the parchment is cut (be careful!). Squeeze the limes over the fish and serve.
