Preheat oven to 450 degrees.
Fold two 13-by-19-inch sheets of parchment in half from short ends to create a crease in each; unfold.
Place each fillet to one side of a sheet, abutting crease; generously season with salt and pepper.
Scatter mushrooms, asparagus, and onion evenly around fillets.
Drizzle each fillet with 2 tablespoons wine.
Scatter butter evenly over fish and vegetables; season with salt and pepper.
Fold each sheet over fish and vegetables.
Starting on one side, roll bottom side of parchment up and over top side to seal; continue working around until pouch is sealed in a half-moon shape.
Transfer both pouches to a rimmed baking sheet.
Steam-roast until parchment puffs and darkens slightly and fish is just cooked through, 10 to 12 minutes.
Carefully rip open pouches (scalding steam will be released) and serve.
