Before you start: You’ll be making 2 partially-wrapped parchment packets. The ingredients are divided evenly between the 2 packets. The measured salt and pepper are also divided between the 2 salmon fillets. Lightly season the vegetables separately with a small extra sprinkle of salt and pepper.
Preheat the oven: Preheat the oven to 400°F (200°C). Line a large sheet pan with foil. Cut 2 pieces of parchment paper, about 16½ x 12¾ inches each.
Remove the skin: If your salmon fillets have skin on, use a sharp knife to remove it, then pat the fillets dry.
Make the miso butter: In a small bowl, mash together the ghee (or softened butter), miso paste, and grated garlic until smooth.
Prepare the vegetables: Slice the zucchini and yellow squash into small rounds. Trim off the root end of the beech mushrooms, then gently separate them with your hands. If using button mushrooms, quarter them.
Assemble the packets: Lay 1 piece of parchment paper for each portion on top of the foil-lined sheet pan. Arrange the zucchini, yellow squash, and mushrooms in a single layer in the center of each parchment sheet. Drizzle lightly with olive oil and season with a small sprinkle of salt and pepper.
Season the fish: Place 1 salmon fillet over each bed of vegetables. Drizzle each fillet with sake, then season with the divided salt, black pepper, and brown sugar. Spread the miso butter evenly over the top of each fillet.
Wrap the packets: Wrap each packet in a candy-wrapper style. Bring the two short ends of the parchment inward and twist them tightly like a wrapped candy, leaving the center open at the top. The parchment should sit up around the salmon like a loose boat, which helps protect the fish from drying out while allowing excess steam to escape.
Bake: Bake on the center rack for 12 to 13 minutes, checking at 12 minutes. The salmon should look opaque and flake easily, with a faint blush in the center.
Serve: Carefully open the parchment packets and watch for hot steam. Spoon the melted miso butter and juices over the fish and vegetables. Garnish with scallions and serve warm.
Notes
Make-ahead: You can mix the miso, ghee or butter, and grated garlic up to 1 week ahead. Store it in the fridge, then let it soften until spreadable before using.